Ch.1 - Intro to General ChemistrySee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Jules Bruno

Every measurement or calculation we do with instruments in chemistry has some level of uncertainty called experimental error. Significant figures are necessary to communicate a level of accuracy and precision while dealing with this uncertainty. 



Rules for Number of Signficant Figures

Rule 1: If your number has a decimal point move from left to right. Start counting once you get to your first non-zero number and keep counting until you get to the end.

Significant-Figures-Decimal-PointsSignficant Figures with Decimal Points

Trailing zeros are a sequence of zeros after the decimal point once you’ve passed all non-zero integers. They would be significant. 

Rule 2: If your number has NO decimal point move from right to left. Start counting once you get to your first non-zero number and keep counting until you get to the end.

Significant-Figures-No-Decimal-PointsSignificant Figures (No Decimal Points)If a value has no decimal point then the final zero would mean it has an infinite number of significant figures. 

Exact Numbers 

Exact numbers contain an infinite number of significant figures because they represent the amount of a particular item and not a measurement. 

For example, when we say that a decade is equal to 10 years, there are 150 students in your chemistry class, or NH3 contains 1 atom of nitrogen and 3 atoms of hydrogen.


Addition & Subtraction

When dealing with addition or subtraction the least number of decimal places will determine the final answer. 

Significant-Figures-AdditionSignificant Figures (Addition)Adding the two values gives the initial value of 5.375 x 106, but the final answer should have only 1 decimal place and so the answer is rounded. 


Multiplication & Division

When dealing with multiplication or division the least number of significant figures will determine the final answer. 

Significant-Figures-MultiplicationSignificant Figures (Multiplication)

Multiplying the two values gives an initial value of 103.6, but you must round your final answer to significant figures.  

Furthermore keep in mind when dealing with mixed operations we must follow the same arithmetic guidelines as we always do. 

Logarithm & Natural Logarithm

When taking the log or ln of a value, the number of significant figures it has determines the number of digits  after the decimal point for the answer.

                  Logarithms-Significant-FiguresSignificant Figures (Logarithms)                             

Using your calculator, the log of 1.53 x 10-3 gives an initial value of - 2.01531. The value of 1.53 x 10-3 has 3 significant figures and so the final answer should have 3 digits after the decimal point. 


Jules Bruno

Jules felt a void in his life after his English degree from Duke, so he started tutoring in 2007 and got a B.S. in Chemistry from FIU. He’s exceptionally skilled at making concepts dead simple and helping students in covalent bonds of knowledge.


Additional Problems
While standing on the summit, you discover there are 16 other people on the top of Africa with you. This number of people has how many significant digits? A) 1 B) 2 C) 3 D) 4 E) unlimited
Give the correct number of significant figures for the following computation: a) 1 b) 2 c) 3 d) 4 e) 5
How many significant figures are in the measurement, 20.300 m? A) 3 B) 4 C) 5 D) 1 E) 2
Solve and give the correct number of significant figures to the problem below. 5.80 x 10 –1 – 3.4 x 10 –2 = A) 5.5 x 10 –2 B) 2.4 x 10 2 C) 5.46 x 10 –1 D) 2.4 x 10 –3 E) 5.5 x 10 –1
Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.
Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance. 
Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance. 
How many significant figures are in each number? a. 0.000312 m b. 312,000 s c. 3.12 X 105 km d. 13,127 s e. 2000
What is the value for y, rounded correctly and to the proper number of significant figures when x = 0.320 in the following equation? y = 7.3562 x - 0.14 a. 2.2 b. 2.214 c. 2.2140 d. 2.21 e. 2.2138
Indicate the number of significant figures in each number. If the number is an exact number, indicate an unlimited number of significant figures.  a. 305,435,087 (2008 U.S. population)  b. 2.54 cm = 1 in  c. 11.4 g/ cm3 (density of lead)  d. 12 = 1 dozen
Round each number to four significant figures. a. 156.182 b. 156.842 c. 156.849 d. 156.899
Consider the addition of 15.4 to 28. What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.
Round each number to three significan t figures. a. 79,845.82 b. 1.548937 X 107 c. 2.3499999995  d. 0.000045389     
Consider multiplying 26.2 by 16.43. What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.
Calculate to the correct number of significant figures.  a. 89.3 X 77.0 X 0.08 
Calculate to the correct number of significant figures.  b. (5.01 X 105) ÷ (7.8 X 102) 
Calculate to the correct number of significant figures.  c. 4.005 X 74 X 0.007 
Calculate to the correct number of significant figures.  d. 453 ÷ 2.031 
Calculate to the correct number of significant figures.  a. 43.7 - 2.341 
Calculate to the correct number of significant figures. b. 17.6 + 2.838 + 2.3 + 110.77 
Calculate to the correct number of significant figures. c. 19.6 + 58.33 - 4.974
Calculate to the correct number of significant figures. d. 5.99 - 5.572
Calculate to the correct number of significant figures.  a. [( 1.7 X 106) ÷ (2.63 X 105)] + 7.33 
Calculate the following to the correct number of significant figures. a) 2 b) 1.5 c) 1.51 d) 1.510  e) 1.5103
Calculate to the correct number of significant figures.  b. (568.99 - 232.1) ÷ 5.3
Calculate to the correct number of significant figures. d. (3.14 X 2.4367) - 2.34  
At 4.000°C water’s density is 1.000 g/cm 3. For the range of temperatures associated with “room temperature” the density of pure water is: Density (g/cm 3) = (-0.00030 (g/°C • cm 3) x Temperature (°C) + 1.0042 (g/cm 3) Based on this thermometer reading, how many significant figures should you report for the calculated density? a) One                   b) Two                  c) Three                   d) Four                 e) Five
Calculate to the correct number of significant figures.  c. (9443 + 45 - 9.9) X 8.1 X 106
Perform the following calculation to the right number of sig figs: a) 1 b) 2 c) 3 d) 4
Which of the following numbers has the greatest number of significant figures? A. 1.500                   B. 2.4 x 10   4                   C. 0.00085                   D. 752,000
What is the correctly reported mass of water based on this data?  (A) 1.3 g (B) 1.30 g (C) 1.298 g (D) 1.2980 g
What is the correct reading for the liquid in this buret? (A) 32 mL (B) 32.2 mL (C) 32.26 mL (D) 33.74 mL
How many significant figures are in the following? 6.022 x 1023 = 340384 = 10.00 = 8.1000 = 0.00000000003 =
There are 6 significant figures in the number 0.003720. A. True B. False
Read the water level with the correct number of significant figures. A) 5 mL B) 5.4 mL C) 5.42 mL D) 5.420 mL E) 5.4200 mL
Read the length of the metal bar with the correct number of significant figures. A) 20 cm B) 15 cm C) 15.1 cm D) 15.10 cm E) 15.100 cm
Give the answer with correct significant figures. 4.56 / (7.49 + 5.493 - 5.345)        
How many significant figures are in 1009.630 mL? A) 3 B) 4 C) 5 D) 6 E) 7
Which measurement is correct when using a 30-cm ruler with 0.1 cm markings?  a)  10.1 cm  b) -0.05 cm     c)   5.225 cm d)  3.45 cm  e) 29 cm
What answer should be reported, with the correct number of significant figures, for the following calculation? (965.43 × 3.911) + 9413.4136 A) 13189 B) 13189.2 C) 1.32 × 104 D) 1.3 × 104 E) 1.319 × 104
Do each calculation without using your calculator and give the answers to the correct number of significant figures.  1.76 X 10- 3 /  8.0 X 102 
Do each calculation without using your calculator and give the answers to the correct number of significant figures.  b. 1.87 X 10- 2 + 2 X 10- 4 - 3.0 X 10-3 
Do each calculation without using your calculator and give the answers to the correct number of significant figures. [(1.36 X 105)(0.000322)/ 0.082](129.2) 
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. How many significant figures are in each of the following numbers?0.1111 s
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. How many significant figures are in each of the following numbers?0.007 m
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. How many significant figures are in each of the following numbers?108,700 km
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. How many significant figures are in each of the following numbers?1.563300 1011
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. How many significant figures are in each of the following numbers?30,800
You weigh an object on a balance and read the mass in grams according to the picture. How many significant figures are in this measurement?
The mass of a glass beaker is known to be 24.8 g. Approximately 5 mL of water are added, and the mass of the beaker and water is measured on an analytical balance to be 30.625 g. How many significant figures are there in the mass of the water?
How many significant figures are in each of the following measurements?35.0445 g
Provide a corrected version for the following statement:The number 0.0033 has more significant figures than 0.033.
How many significant figures are in each of the following measurements?59.0001 cm
How many significant figures are in each of the following measurements?0.03003 kg
How many significant figures are in each of the following measurements?0.00450 m
How many significant figures are in each of the following measurements?67,000 m2
The following statements are all true. a. Jessicas house is 5 km from the grocery store. b. Jessicas house is 4.73 km from the grocery store. c. Jessicas house is 4.73297 km from the grocery store.What does the number of digits in each statement communicate?
You may want to reference (Pages 411 - 412) Section 1.6 while completing this problem.How many significant figures should be reported for the volume of the metal bar shown below?
What is the number of significant figures in each of the following measured quantities?601 kg
How many significant figures are in each number?1,050,501 km
What is the number of significant figures in each of the following measured quantities?0.054 s
How many significant figures are in each number?0.00020 m
What is the number of significant figures in each of the following measured quantities?6.3050 cm
How many significant figures are in each number?0.005710 s
What is the number of significant figures in each of the following measured quantities?0.0105 L
How many significant figures are in each number?0.001090 cm
How many significant figures are in each number?180,701 mi
What is the number of significant figures in each of the following measured quantities?400 g
How many significant figures are in each number?0.01040 m
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.3.774 km
How many significant figures are in each number?0.005710 km
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.205 m2
How many significant figures are in each number?90,201 m
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.1.700 cm
How many significant figures are in each of the following numbers?0.000312 m
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.350.00 K
How many significant figures are in each of the following numbers?312,000 s
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.307.080 g
How many significant figures are in each of the following numbers?3.12 105
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Indicate the number of significant figures in each of the following measured quantities.1.3 m/s 103 { m m/s}
How many significant figures are in each of the following numbers?13,127 s
How many significant figures are in each of the following numbers?2000
Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?= 3.14
Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?12 inches = 1 foot
Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?EPA gas mileage rating of 26 miles per gallon
Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?1 gross = 144
Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.284,796,887 (2001 U.S. population)
Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.2.54 cm = 1 in
Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.11.4 g/cm3 (density of lead)
Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.12 = 1 dozen
How many significant figures does each of the following quantities have?76.600 kJ
How many significant figures does each of the following quantities have?3000 nm
How many significant figures does each of the following quantities have?0.00300 mL
How many significant figures does each of the following quantities have?18 students
A temperature measurement of 25oC has three significant figures, while a temperature measurement of -196oC has only two significant figures.Explain.
You may want to reference (Pages 24 - 28)Section 1.6 while completing this problem.An object is determined to have a mass of 0.01080 g. How many significant figures are there in this measurement?
How many significant figures does each of the following quantities have?47.60 mL
How many significant figures does each of the following quantities have?2070 mi
Is the use of significant figures in each of the following statements appropriate?On July 1, 2005, the population of Cook County, Illinois, was 5,303,683.
Is the use of significant figures in each of the following statements appropriate?In the United States, 0.621 % of the population has the surname Jones.
Is the use of significant figures in each of the following statements appropriate?You calculate your grade point average to be 3.87532.
A sample that has a mass of about 25 g is weighed on a balance that has a precision of 0.1 g. How many significant figures should be reported for this measurement?
Carry out the following operations, and express the answer with the appropriate number of significant figures. You may want to reference(Pages 24 - 28)Section 1.6 while completing this problem.320.55 - (6105.5/2.6)
Perform the following calculations to the correct number of significant figures.(86.6 - 23.501) 0.0051
Perform the following calculations to the correct number of significant figures.[(2.51106) 47.501] + 145.01
Perform the following calculations to the correct number of significant figures.[(1.8106) (2.66105)] + 7.51
Perform the following calculations to the correct number of significant figures.(550.01 - 225.1) 5.4
Perform the following calculations to the correct number of significant figures.(9453 + 47 - 7.5) (8.3106)
You may want to reference (Page 23) Section 1.7 while completing this problem.Perform the calculation to the correct number of significant figures. (8.02 - 7.60) /3.003
Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance. You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem.
Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance. You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem.
Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance. You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem.
What is the temperature reading on the Celsius thermometer? (The perspective is not technically ideal, readings should be done at eye-level with the meniscus.)
How many milliliters of water does the graduated cylinder in (a) contain?
How tall in centimeters is the paper clip in (b)?
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem.Record the temperature on the thermometer shown here to the correct number of digits.
What is the meaning of the number of digits reported in a measured quantity?
The following statements are all true. a. Jessicas house is 5 km from the grocery store. b. Jessicas house is 4.73 km from the grocery store. c. Jessicas house is 4.73297 km from the grocery store.What sort of device would Jessica need to make the measurement in each statement?
What is the length of the pencil in the figure if the scale reads in centimeters?
An oven thermometer with a circular scale reading degrees Fahrenheit is shown. What temperature does the scale indicate?
Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.
Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.
Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.
Read the volume of the cylinder and report your answer to the correct number of significant figures. The volume is indicated by the bottom of the meniscus.
The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures, and express it in standard exponential notation.
The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures, and express it in standard exponential notation.
You may want to reference (Pages 21 - 26) section 1.7 while completing this problem. Round each to three significant figures.79850.02
What is the following number to four significant figures in standard exponential notation: 102.53070
You may want to reference (Pages 21 - 26) section 1.7 while completing this problem. Round each to three significant figures.1.548952×107
What is the following number to four significant figures in standard exponential notation: 656,980
You may want to reference (Pages 21 - 26) section 1.7 while completing this problem. Round each to three significant figures.2.34975001
What is the following number to four significant figures in standard exponential notation: 0.008543210
What is the following number to four significant figures in standard exponential notation: 0.000257870
What is the following number to four significant figures in standard exponential notation: -0.0357202
What are the rules for rounding off the results of calculations?
The diameter of Jupiter at its equator is 142984 km.Round off this quantity to four significant figures.
The diameter of Jupiter at its equator is 142984 km.Round off this quantity to two significant figures.
Round off the following quantities to the number of significant figures indicated in parentheses.3.567006×104 m (4)
Round off the following quantities to the number of significant figures indicated in parentheses.70.427 g (2)
The following statements are all true. a. Jessicas house is 5 km from the grocery store. b. Jessicas house is 4.73 km from the grocery store. c. Jessicas house is 4.73297 km from the grocery store.How can all the statements be true?
Round off the following quantities to the number of significant figures indicated in parentheses.4936 cm (3)
Round off the following quantities to the number of significant figures indicated in parentheses.2.30003×10−4 kg (5)
Round off the following quantities to the number of significant figures indicated in parentheses.3.567006×104 m (6)
Round off the following quantities to the number of significant figures indicated in parentheses.70.427 g (3)
Round off the following quantities to the number of significant figures indicated in parentheses.6.5004 kg (4)
Round off the following quantities to the number of significant figures indicated in parentheses.1.904 km (3)
Round off the following quantities to the number of significant figures indicated in parentheses.13.0004 g/cm3 (3)
Round off the following quantities to the number of significant figures indicated in parentheses.2.2500004×106 (7)
Round each of the following numbers to four significant figures.155.052
Round each of the following numbers to four significant figures.155.042
Round each of the following numbers to four significant figures.155.049
Round each of the following numbers to four significant figures.155.099
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Carry out the following operations, and express the answers with the appropriate number of significant figures.0.0589 / 0.678
You may want to reference (Pages 21 - 26) section 1.7 while completing this problem. Calculate the following to the correct number of significant figures.(5.01105)  (8.2102)
When multiplying or dividing measured quantities, what determines the number of significant figures in the result?
Perform the following calculations to the correct number of significant figures.(2.210106) (7.1104)
Carry out the following calculations, expressing each result with the correct number of significant figures:4.6742 g / 0.003 71 L = ? g/L
Do each calculation and give the answers to the correct number of significant figures.1.7610-3/8.1102
Do each calculation and give the answers to the correct number of significant figures.[(1.35105)(0.000351)/0.083](122.1)
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Carry out the following operations, and express the answers with the appropriate number of significant figures.14.3505 + 2.66
You may want to reference (Pages 24 - 28) Section 1.6 while completing this problem. Carry out the following operations, and express the answers with the appropriate number of significant figures.952.8 - 140.7389
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. Perform the following calculations to the correct number of significant figures.0.004 + 0.09853
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. Perform the following calculations to the correct number of significant figures.1250.5 + 7.50 + 6.00
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. Perform the following calculations to the correct number of significant figures.2.5 - 1.803
You may want to reference (Pages 21 - 26) Section 1.7 while completing this problem. Perform the following calculations to the correct number of significant figures.562 + 7.1 - 50.003
What is the difference in mass between a nickel that weighs 4.8 g and a nickel that weighs 4.870 g ?
When adding or subtracting measured quantities, what determines the number of decimal places in the result?
A table is given below listing the heights of each member in a group. Using the table, perform the following calculations. Use appropriate rules for significant figures at each step. Group Member Height Student 1 4 ft 6.0 in Student 2 5 ft 6.0 in Student 3 5 ft 6.0 in Calculate the sum of all the heights.
Express the results of the following calculations with the correct number of significant figures.5502.4 + 24 + 0.06
Express the results of the following calculations with the correct number of significant figures.86.6 + 1.46 - 0.06
Perform the following calculations to the correct number of significant figures.40.8 - 2.253
Perform the following calculations to the correct number of significant figures.17.6 + 4.518 + 4.6 + 115.01
Perform the following calculations to the correct number of significant figures.20.1 + 60.01 - 5.014
Perform the following calculations to the correct number of significant figures.6.00 - 5.612
Carry out the following calculations, expressing each result with the correct number of significant figures:24.567 g + 0.044 78 g = ? g
Carry out the following calculations, expressing each result with the correct number of significant figures:0.378 mL + 42.3 mL - 1.5833 mL = ? mL
Do each calculation and give the answers to the correct number of significant figures.1.8610-2 + 310-4 - 3.110-3
The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures, and express it in standard exponential notation.
Carry out the following operations, and express the answers with the appropriate number of significant figures.(a) 12.0550 + 9.05
What is the number of significant figures in each of the following measured quantities?(a) 358 kg 
What is the number of significant figures in each of the following measured quantities?(b) 0.054 s 
What is the number of significant figures in each of the following measured quantities?(c) 6.3050 cm 
What is the number of significant figures in each of the following measured quantities?(d) 0.0105 L 
What is the number of significant figures in each of the following measured quantities?(e) 7.0500 x 10–3m3 
Indicate the number of significant figures in each of the following measured quantities:(a) 3.774 km 
Indicate the number of significant figures in each of the following measured quantities: (b) 205 m2
Indicate the number of significant figures in each of the following measured quantities: (c) 1.700 cm 
Indicate the number of significant figures in each of the following measured quantities: (e) 307.080 g 
Indicate the number of significant figures in each of the following measured quantities: (d) 350.00 K 
Carry out the following operations, and express the answers with the appropriate number of significant figures.(b) 257.2 - 19.789 
Carry out the following operations, and express the answers with the appropriate number of significant figures.(e) (6.21 x 103) (0.1050) 
Carry out the following operations, and express the answers with the appropriate number of significant figures.(d) 0.0577/ 0.753 
Carry out the following operations, and express the answer with the appropriate number of significant figures.(a) 320.5 - (6104.5/2.3)
Carry out the following operations, and express the answer with the appropriate number of significant figures.(b) [(285.3 x 105) – (1.200 x 103)] x 2.8954
Carry out the following operations, and express the answer with the appropriate number of significant figures.(c) (0.0045 x 20,000.0) + (2813 x 12)
You weigh an object on a balance and read the mass in grams according to the picture. How many significant figures are in this measurement?
You have a graduated cylinder that contains a liquid (see photograph). Write the volume of the liquid, in milliliters, using the proper number of significant figures.
For each number, underline the zeroes that are significant and draw an x through the zeroes that are not:a. 1,050,501 km b. 0.0020 mc. 0.000000000000002 s d. 0.001090 cm  
 All 50 students agree that in the classroom there are 100 chairs. This number has: a. 1 significant figure b. 2 significant figures c. 3 significant figures d. Infinite number of significant figures e. We cannot know with the available information
How many significant figures are in each of the following?a. 100
How many significant figures are in each of the following?b. 1.0 x 10 2
How many significant figures are in each of the following?c. 1.0 x 10 3
How many significant figures are in each of the following?d. 100.
How many significant figures are in each of the following?e. 0.0048
How many significant figures are in each of the following?f. 0.00480
How many significant figures are in each of the following?g. 4.80 x 10–3
How many significant figures are in each of the following?g. 4.800 x 10–3
Evaluate each of the following and write the answer to the appropriate number of significant figures.a. 212.2 + 26.7 + 402.09
Evaluate each of the following and write the answer to the appropriate number of significant figures.b. 1.0028 + 0.221 + 0.10337
Evaluate each of the following and write the answer to the appropriate number of significant figures.c. 52.331 + 26.01 - 0.9981
(a) What is the length of the pencil in the following figure if the scale reads in centimeters? How many significant figures are there in this measurement? 
Evaluate each of the following and write the answer to the appropriate number of significant figures.d. 2.01 x 102 + 3.014 x 103
(b) An oven thermometer with a circular scale reading degrees Fahrenheit is shown. What temperature does the scale indicate? How many significant figures are in the measurement? [Section 1.5] 
Evaluate each of the following and write the answer to the appropriate number of significant figures.e. 7.255 - 6.8350
Perform the following mathematical operations, and express each result to the correct number of significant figures.a. 0.102 x 0.0821 x 273 / 1.01
Perform the following mathematical operations, and express each result to the correct number of significant figures.b. 0.14 x 6.022 x 10 23
Perform the following mathematical operations, and express each result to the correct number of significant figures.c. 4.0 x 10 4 x 5.021 x 10-3 x 7.34993 x 102
(a) How many significant figures should be reported for the volume of the metal bar shown below? [5ection 1.5] 
Perform the following mathematical operations, and express each result to the correct number of significant figures.d. 2.00 x 106 / 3.00 x 10 -7
Perform the following mathematical operations and express the result to the correct number of significant figures.a. 2.526 / 3.1 + 0.470 / 0.623 + 80.705 / 0.4326
Perform the following mathematical operations and express the result to the correct number of significant figures.b. (6.404 x 2.91) / (18.7 - 17.1)
Perform the following mathematical operations and express the result to the correct number of significant figures.c. 6.071 x 10-5 - 8.2 x 10-6 - 0.521 x 10-4
Perform the following mathematical operations and express the result to the correct number of significant figures.d. (3.8 x 10-12 + 4.0 x 10-13) / (4 x 1012 + 6.3 x 1013)
Perform the following mathematical operations and express the result to the correct number of significant figures.e. 9.5 + 4.1 + 2.8 + 3.175 / 4(Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.)
Perform the following mathematical operations and express the result to the correct number of significant figures.f. 8.925 - 8.905 / 8.925 x 100(This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)
The number of significant figures in 0.066900 x 10 -4 isa. 5b. 6c. 7d. 3e. 4
What is the correct answer to the following expression? 4.13 x 10-10 + 7.59 x 10 -12 a. 4.21 x 10-10 b. 4.2 x 10-10 c. 4 x 10-10 d. 4.206 x 10-10 e. 4.2059 x 10-10 
Read the length of the metal bar with the correct number of significant figures. A) 20 cm B) 15 cm C) 15.1 cm D) 15.10 cm E) 15.100 cm
How many significant figures should be used to express the value of x? x = (23.714 + 86.97 - 0.8693) / 31.7400 ? A) two B) three C) four D) five E) six
Determine the number of significant figures for the result of the following arithmetic calculations. (i) (332.41 + 711.59) (ii) (3.00 x 92.11) / 1.250 (iii) [(25.01 x 6.0) + 40.11] A) 6, 3, 2 B) 4, 3, 3 C) 5, 3, 2 D) 5, 4, 3 E) 5, 3, 4
How many significant figures are contained in each of the following measurements?(c) 86,002 J
How many significant figures are contained in each of the following measurements?(d) 9.740 × 104 m/s
How many significant figures are there in each of the following values?d. 8 x 108
How many significant figures are contained in each of the following measurements?(e) 10.0613 m3 
How many significant figures are there in each of the following values?e. 463.8052
How many significant figures are contained in each of the following measurements? (f) 0.17 g/mL
How many significant figures are contained in each of the following measurements?(g) 0.88400 s
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(b) 12 tablets
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(c) 3% hydrogen peroxide
How many significant figures are there in each of the following values?f. 300
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(d) 5.5 ounces
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(e) 473 mL
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(f) 1.75% bismuth
How many significant figures are there in each of the following values?g. 301
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(g) 0.001% phosphoric acid
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(h) 99.80% inert ingredients
How many significant figures are there in each of the following values?h. 300.
How many significant figures are in each of the following?a. 100
How many significant figures are in each of the following?b. 1.0 x 102
How many significant figures are in each of the following?c.  1.00 x 103
How many significant figures are in each of the following?d. 100.
How many significant figures are in each of the following?e. 0.0048
How many significant figures are in each of the following?f. 0.00480
How many significant figures are in each of the following?g. 4.80 x 10-3
How many significant figures are in each of the following?h. 4.800 x 10-3
How many significant figures are in each of the following measurements?3.8200 x 103 km
Underline the significant zero(s) in the following number:• 0.041
Underline the significant zero(s) in the following number:• 0.0410
Underline the significant zero(s) in the following number:• 4.0100 x 104
Underline the significant zero(s) in the following number:• 508
Underline the significant zero(s) in the following number:• 5.080 x 103
Underline the significant zero(s) in the following number:• 0.05080
How many significant figures does each of the following quantities have?4.50200 x 103 g
How many significant figures does each of the following quantities have?3 x 10-5 g
Which statements include exact numbers?(a) Angel Falls is 3212 ft high.(b) There are 8 known planets in the Solar System.(c) There are 453.59 g in 1 lb.(d) There are 1000 mm in 1 m.
Which of the following include exact numbers?(a) The speed of light in a vacuum is a physical constant; to six significant figures, it is 2.99792 x 108 m/s.(b) The density of mercury at 25°C is 13.53 g/mL.(c) There are 3600 s in 1 h.(d) In 2016, the United States had 50 states.
Underline the significant zero(s) in the following number:• 0.41
Underline the significant zero(s) in the following number:• 5.08
Indicate the number of significant figures in each of the following:a. This book contains more than 1000 pages.
Indicate the number of significant figures in each of the following:b. b. A mile is about 5300 ft.
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(a) the number of eggs in a basket
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(a) the number of seconds in an hour
Indicate the number of significant figures in each of the following:c. A liter is equivalent to 1.059 qt.
How many significant figures are contained in each of the following measurements?(a) 38.7 g(b) 2 × 1018 m(c) 3,486,002 kg(d) 9.74150 × 10−4 J(e) 0.0613 cm3(f) 17.0 kg(g) 0.01400 g/mL
How many significant figures are contained in each of the following measurements?(a) 53 cm
The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(a) 0.0055 g active ingredients
Indicate the number of significant figures in each of the following:d. The population of the United States in 2015 is 3.1 x 102 million.
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(b) the mass of a dozen eggs
Indicate the number of significant figures in each of the following:e. A kilogram is 1000 g.
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(c) the number of gallons of gasoline necessary to fill an automobile gas tank
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(d) the number of cm in 2 m
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(e) the mass of a textbook
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h
Indicate the number of significant figures in each of the following:f. The Boeing 747 cruises at around 600 mi/h.
How many significant figures are there in each of the following values?a. 6.07 x 10-15
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(b) the number of pages in this book
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(c) the number of grams in your weight
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(d) the number of grams in 3 kilograms
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(e) the volume of water you drink in one day
Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(f) the distance from San Francisco to Kansas City
How many significant figures are contained in each of the following measurements?(b) 2 × 1018 m
How many significant figures are there in each of the following values?b. 0.003840
How many significant figures are contained in each of the following measurements?(c) 3,486,002 kg
How many significant figures are contained in each of the following measurements?(d) 9.74150 × 10−4 J
How many significant figures are contained in each of the following measurements?(e) 0.0613 cm3
How many significant figures are contained in each of the following measurements?(f) 17.0 kg
How many significant figures are contained in each of the following measurements?(g) 0.01400 g/mL
How many significant figures are contained in each of the following measurements?(b) 2.05 × 108 m
How many significant figures are there in each of the following values?c. 17.00
Perform the following mathematical operations and express the result to the correct number of significant figures.a. 
Perform the following mathematical operations and express the result to the correct number of significant figures.b. (6.404 x 2.91) / (18.7 - 17.1)
Perform the following mathematical operations and express the result to the correct number of significant figures.c. 6.071 x 10-5 - 8.2 x 10-6 - 0.521 x 10-4
Perform the following mathematical operations and express the result to the correct number of significant figures.d. (3.8 x 10-12 + 4.0 x 10-13) / (4 x 1012 + 6.3 x 1013) 
Perform the following mathematical operations and express the result to the correct number of significant figures.e. (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.)
Perform the following mathematical operations and express the result to the correct number of significant figures.f. (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)
Perform the following mathematical operations, and express the result to the correct number of significant figures.c. 1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1
Perform the following mathematical operations, and express the result to the correct number of significant figures.d. 
Perform the following mathematical operations, and express the result to the correct number of significant figures.e. 
Perform the following mathematical operations, and express the result to the correct number of significant figures.f. 
Perform the following calculations and report each answer with the correct number of significant figures.(h) 
Carry out the following calculation, making sure that your answer has the correct number of significant figures:
Evaluate each of the following and write the answer to the appropriate number of significant figures.d. 2.01 x 102 + 3.014 x 103
The beakers shown below have different precisions.a. Label the amount of water in each of the three beakers to the correct number of significant figures.
Which of the following are exact numbers?a. There are 100 cm in 1 m.b. One meter equals 1.094 yards.c. We can use the equation  to convert from Celsius to Fahrenheit temperature. Are the numbers  and 32 exact or inexact?d. π = 3.1415927.
Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water, and explain your answers (the numbers given are as precise as possible).a. 128.7 mL
Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water, and explain your answers (the numbers given are as precise as possible).b. 18 mL
Round off each of the following numbers to two significant figures:(a) 0.436
Round off each of the following numbers to two significant figures:(b) 9.000
Round off each of the following numbers to two significant figures:(c) 27.2
Round off each of the following numbers to two significant figures:(d) 135
Round off each of the following numbers to two significant figures:(f) 0.445
Round off each of the following numbers to two significant figures:(e) 1.497 × 10−3 
You may want to reference (Pages 21 - 26) section 1.7 while completing this problem.Round each to three significant figures.0.000045419
Round off each of the following numbers to two significant figures:(a) 517
Round off each of the following numbers to two significant figures:(b) 86.3
Round off each of the following numbers to two significant figures:(c) 6.382 × 103 
Round off each of the following numbers to two significant figures:(d) 5.0008
Round off each of the following numbers to two significant figures:(e) 22.497
Round off each of the following numbers to two significant figures:(f) 0.885
Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.a. 0.00034159 to three digits
Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.b. 103.351 x 102 to four digits
Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.c. 17.9915 to five digits
Round off each of the following numbers to the indicated number of significant digits and write the answer in standardscientific notation.d. 3.365 x 105 to three digits
Use exponential notation to express the number 385,500 toa. one significant figure.
Use exponential notation to express the number 385,500 tob. two significant figures.
Use exponential notation to express the number 385,500 toc. three significant figures.
Use exponential notation to express the number 385,500 tod. five significant figures.
Round off the number to the indicated number of significant figures (sf): 35.8348 (to 4 sf)
Round off each number to the indicated number of significant figures (sf): 22.4555 (to 3 sf)
Round off the number to the indicated number of significant figures (sf): 0.00845 (to 2 sf)
Round off the number to the indicated number of significant figures (sf): 144,000 (to 2 sf)
Round off the number to the indicated number of significant figures (sf): 0.0003554 (to 2 sf)
Round off the number to the indicated number of significant figures (sf): 231.554 (to 4 sf)
Round off each number in the following calculation to one fewer significant figure, and find the answer:
Round off each number in the following calculation to one fewer significant figure, and find the answer:
Perform the following calculations and report each answer with the correct number of significant figures. (a) 628 × 342
Perform the following calculations and report each answer with the correct number of significant figures.(b) (5.63 × 102 ) × (7.4 × 103 )
Perform the following calculations and report each answer with the correct number of significant figures.(c) 
Perform the following calculations and report each answer with the correct number of significant figures.(d) 8119 × 0.000023
Perform the following mathematical operations, and express the result to the correct number of significant figures.a. 6.022 x 1023 x 1.05 x 102
Perform the following mathematical operations, and express the result to the correct number of significant figures.b. 
Perform the following calculations and report each answer with the correct number of significant figures.(a) 62.8 × 34
Perform the following calculations and report each answer with the correct number of significant figures.(c) 38 × 95 × 1.792
Perform the following calculations and report each answer with the correct number of significant figures.(e) 
Carry out the following calculation, making sure that your answer has the correct number of significant figures:V = πr 2h, where r = 6.23 cm and h = 4.630 cm
Carry out the following calculation, making sure that your answer has the correct number of significant figures:
Perform the following mathematical operations, and express each result to the correct number of significant figures.a. 
Perform the following mathematical operations, and express each result to the correct number of significant figures.b. 0.14 x 6.022 x 1023
Perform the following mathematical operations, and express each result to the correct number of significant figures.c. 4.0 x 104 x 5.021 x 10-3 x 7.34993 x 102
Perform the following mathematical operations, and express each result to the correct number of significant figures.d. 
Perform the following calculations and report each answer with the correct number of significant figures.(e) 14.98 + 27,340 + 84.7593
Perform the following calculations and report each answer with the correct number of significant figures.(f) 42.7 + 0.259
Perform the following calculations and report each answer with the correct number of significant figures.(b) 0.147 + 0.0066 + 0.012
Perform the following calculations and report each answer with the correct number of significant figures.(d) 15 – 0.15 – 0.6155
Perform the following calculations and report each answer with the correct number of significant figures.(f) 140 + 7.68 + 0.014
Perform the following calculations and report each answer with the correct number of significant figures.(g) 28.7 – 0.0483
Carry out the following calculation, making sure that your answer has the correct number of significant figures:1.110 cm + 17.3 cm + 108.2 cm + 316 cm
The beakers shown below have different precisions.c. Suppose you pour the water from these three beakers into one container. What should be the volume in the container reported to the correct number of significant figures?
Evaluate each of the following and write the answer to the appropriate number of significant figures.a. 212.2 + 26.7 + 402.09
Evaluate each of the following and write the answer to the appropriate number of significant figuresb. 1.0028 + 0.221 + 0.10337
Evaluate each of the following and write the answer to the appropriate number of significant figures.c. 52.331 + 26.01 - 0.9981
Evaluate each of the following and write the answer to the appropriate number of significant figures.e. 7.255 - 6.8350
Express 96,342 m using 2 significant figures. 1) 9.60 104 m 2) 9.6 10-4 m 3) 9.6 104 m 4) 96,000. m 5) 9.60 10-4  m
Translate the following numbers into standard notation, maintaining the same number of significant figures. a. 4.52 x 103 b.  8.11 x 10-2 
How many significant figures are in the number 0.80610?
How many significant digits are in the following number? 150.0
Which measurement is expressed to 4 significant figures? 1) 0.00423 kg 2) 24.049 cm 3) 1300 K 4) 82,306 m5) 62.40 g
Identify the exact numbers in this list. Select all that apply. (a) 56.00 s (a time measured by a stopwatch) (b) 4 choices (the number of choices in this list) (c) 2.54 cm (the number of centimeters in exactly 1 in) (d) 3 lbs (the weight of an object measured on a scale)