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**Significant Figures** are used to determine some level of accuracy within our recorded measurements.

Concept #1: Determining significant figures

**Transcript**

We're going to say that we know that there is some level of accuracy and precision necessary with all of our calculations. But when we get an answer, how many digits does that answer have to have? That's when significant figures come into play and play a very important role in deciding the number of digits in our answer.

Now sig figs can be really easy as long as we remember two simple rules. It has to do with decimal places or no decimal places. Let's take a look at these two rules.

We're going to say rule one has to do with if you have a decimal point. We're going to say, if your number has a decimal point, we're going to move from left to right, so we're going to move from left to right. We're going to start counting once we get to our first non-zero number and keep counting until we get to the very end.

Now, rule number two is, if our number has no decimal point. If it has no decimal point, then you're going to start moving from right to left. We're going to start counting once we get to our first non-zero number and keep counting until you get to the very end.

Now, that we've seen these two simple rules, let's apply them to these examples.

Example #1: How many sig figs does each number contain?

0.0000185 m 749 mol

17.3 x 10** ^{3}** mL 100

0.0010050 kg 1560 mol

Example #2: Read the length of the metal bar to the correct number of significant figures.

Concept #2: Understanding calculations with Significant Figures

**Transcript**

We’re going to say, when it comes to calculations we separate them into two categories. Multiplication and division go together; addition and subtraction will go together.

So we are going to say here when it comes to multiplication and division, measurements with the least number of significant figures, I’m just going to say sig figs, will determine our final answer. And when it comes to addition and subtraction we are going to say measurements with the least number of decimal places will determine our final answer.

So just remember when we are multiplication or division, we’re looking at the number of sig figs for our measurements. The one with the smallest number of sig figs will determine the number of sig figs in our final answer.

When we are doing addition and subtraction we want to get the fewest number of decimal positions that will give us our final answer.

The number of significant figures involved in a calculation depends on whether we are adding, subtracting, multiplying or dividing.

Example #3: Perform the following calculation to the right number of sig figs:

(3.16) x (0.003027) x (5.7 x 10** ^{-3}**)

Whenever we are adding or subtracting numbers with different exponents we must manipulate them to one common exponent value. We manipulate the values to get the least number of decimal places.

Example #4: Perform the following calculation to the right number of sig figs:

2.628 x 10^{6}

6.281 x 10^{4}

__+ 0.827 x 10__^{7}

Whenever we are dealing with a mixture of functions just remember your order of operations.

Example #5: Perform the following calculation to the right number of sig figs:

__(42.00 – 40.915) • (25.739 – 25.729)__

(11.50 • 1.001) + (0.00710 • 700.)

0 of 7 completed

Concept #1: Determining significant figures

Example #1: How many sig figs does each number contain?
0.0...

Example #2: Read the length of the metal bar to the correct ...

Concept #2: Understanding calculations with Significant Figu...

Example #3: Perform the following calculation to the right n...

Example #4: Perform the following calculation to the right n...

Example #5: Perform the following calculation to the right n...

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

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

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

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

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)

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 –2B) 2.4 x 10 2C) 5.46 x 10 –1D) 2.4 x 10 –3E) 5.5 x 10 –1

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 cmB) 15 cmC) 15.1 cmD) 15.10 cmE) 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 in each of the following numbers?1.563300 1011

An object is determined to have a mass of 0.01080 g. How many
significant figures are there in this measurement?

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.

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

Perform the calculations to the correct number of significant figures.(12.01 x imes 0.3) + 4.811

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.b. Is it possible for each of the three beakers to contain the exact same amount of water? If no, why not? If yes, did you report the volumes as the same in part a? Explain.

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 each to three significant figures.1.548952×107

Use exponential notation to express the number 385,500 tod. five significant figures.

Carry out the following operations, and express the answer with the appropriate number of significant figures.863 x [1255 - (3.45 x 108)]

What is the difference in mass between a nickel that weighs 4.8 g and a nickel that weighs 4.870 g ?

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.

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.

How many significant figures are in each of the following measurements?67,000 m2

Compute 4.659×104 − 2.14×104. Round the answer appropriately. Express your answer as an integer using the proper number of significant figures (e.g. 12300).

Consider the numbers 23.68 and 4.12. The sum of these numbers has ____ significant figures, and the product of these numbers has ____ significant figures.

A calculator is used to add and subtract measured masses: 43 g + 1.00 g - 2.008 g = 41.992 g What should the numeric answer be when expressed to the correct number of significant figures?

Carry out the following calculations, expressing each result with
the correct number of significant figures:4.6742 g / 0.00371 L = ? g/L

What is the meaning of the number of digits reported in a measured quantity?

The result of (3.8621 x 1.5630) - 5.98 is properly written asA) 0.056B) 0.056462C) 0.06D) 0.0565E) 0.05646

How many significant digits are in the number 0.002030?a. 3b. 4c. 5d. 6e. 7

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?

What is the length of the pencil in the figure if the scale reads in centimeters?

What is the following number to four significant figures in standard exponential notation: 102.53070

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 milliliters of liquid does the smaller graduated cylinder contain? Express your answer in milliliters using the proper number of significant figures.

What is the correct reading for the liquid in this burette?(A) 32 mL(B) 32.2 mL(C) 32.26 mL(D) 33.74 mL

What is the length of the metal bar with the correct number of significant figures?a. 20 cmb. 15 cmc. 15.0 cmd. 15.00 cme. 15.000 cm

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 cmd) 3.45 cm e) 29 cm

Read the water level with the correct number of significant figures.A) 87.20 mL B) 87.2 mL C) 87.2000 mL D) 87.200 mL E) 87 ml

What is the following number to four significant figures in standard exponential notation: 0.008543210

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.

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

How many significant digits are in the following number? 150.0

A student weighs a flask (222g) and adds to this flask 4.325g of glucose (C6H12O6) and 35.5g of water. Properly expressed in significant figures, the total mass of this flask, sugar and water is now (in grams):a) 261.82b) 261.825c) 262d) 261.8 e) 261

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)

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?35.0445 g

Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?1 gross = 144 pcs

Round off the following quantities to the number of significant figures indicated in parentheses.70.427 g (3)

Which of these best expresses 0.0030950 in exponential notation to three significant figures?

How many significant figures are there in the number 0.0003677?

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

How many significant figures are there in the answer for the following problem?A) one B) two C) three D) four

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?

Carry out the following calculations, expressing each result with
the correct number of significant figures:24.567 g + 0.044 78 g = ? g

The following statements are all true.a.
Jessica's house is 5 km from the grocery store.b.
Jessica's house is 4.73 km from the grocery store.c.
Jessica's house is 4.73297 km from the grocery store.What sort of device would Jessica need to make the measurement in each
statement?

The diameter of Jupiter at its equator is 142984 km.Round off this quantity to four significant figures.

How many significant figures are in the measurement, 0.0005890 g?A. 4B. 5C. 6D. 7E. 8

Which of the following has 4 significant figures?A. 0.0042B. 1.054C. 1.30 x 102D. 1300E. 2.0004

Express 96,342 m using 2 significant figures. 1) 9.60 x 104 m 2) 9.6 x 10-4 m 3) 9.6 x 104 m 4) 96,000. m 5) 9.60 x 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?

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