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

*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

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 NH_{3} 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.

^{6}, but the final answer should have only 1 decimal place and so the answer is rounded. Adding the two values gives the initial value of 5.375 x 10

**Multiplication & Division**

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

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.

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.

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)

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

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)