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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...

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

Give the correct number of significant figures for the following computation:
a) 1
b) 2
c) 3
d) 4
e) 5

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

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

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

Calculate the following to the correct number of significant figures.
a) 2
b) 1.5
c) 1.51
d) 1.510
e) 1.5103

Give the answer with correct significant figures.
4.56 / (7.49 + 5.493 - 5.345)

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

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

How many significant figures are in the measurement, 20.300 m?
A) 3
B) 4
C) 5
D) 1
E) 2

There are 6 significant figures in the number 0.003720.
A. True
B. False

Based on our introductory discussions of matter and measurement, which of the following matching statements is INCORRECT?a) A state of matter that is significantly compressible: gasb) Anything that has mass and takes up space: matterc) Gas to solid conversion: sublimationd) Matter of variable composition: mixturese) The number of significant figures in the measurement 0.00230 m: 3

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 are in the following?6.022 x 1023 =340384 =10.00 =8.1000 =0.00000000003 =

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

What is the correctly reported mass of water based on this data? (A) 1.2980 g(B) 1.298 g(C) 1.30 g(D) 1.3 g

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.

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

How many significant figures are in each number?a. 0.000312 mb. 312,000 sc. 3.12 X 105 kmd. 13,127 se. 2000

Round each number to four significant figures.a. 156.852b. 156.842c. 156.849d. 156.899

Round each number to three significant figures.a. 79,845.82b. 1.548937 X 107c. 2.3499999995 d. 0.000045389

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 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

Calculate to the correct number of significant figures. c. (9443 + 45 - 9.9) X 8.1 X 106

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)

(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]

(a) How many significant figures should be reported for the volume of the metal bar shown below? [5ection 1.5]

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

Indicate which of the following are exact numbers:(a) the mass of a paper clip(b) the surface area of a dime(c) the number of inches in a mile(d) the number of ounces in a pound (e) the number of microseconds in a week (f) the number of pages in this book

Indicate which of the following are exact numbers:(a) the mass of a 32-oz can of coffee(b) the number of students in your chemistry class(c) the temperature of the surface of the sun(d) the mass of a postage stamp(e) the number of milliliters in a cubic meter of water(f) the average height of students in your school

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 10–3 m3

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.

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. 1.00 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

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

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

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.)

Which of the following is NOT an exact number?A) Your weight in pounds.B) The amount of pennies per dollar.C) The number of milligrams in a kilogram.D) The number students in this classroom.

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

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

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

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

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

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

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