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

**Concept:** Determining significant figures

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:** 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

4m **Example:** Read the length of the metal bar to the correct number of significant figures.

**Concept:** Understanding calculations with Significant Figures

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:** 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:** 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:** 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.)

5mAll 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

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There are 6 significant figures in the number 0.003720.

A. True

B. False

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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

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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

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How many significant figures are in the measurement, 20.300 m?

A) 3

B) 4

C) 5

D) 1

E) 2

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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

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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

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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}

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Give the answer with correct significant figures.

- 4.56 / (7.49 + 5.493 - 5.345)

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How many significant figures are in the following?

- 6.022 x 10
^{23}= - 340384 =
- 10.00 =
- 8.1000 =
- 0.00000000003 =

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Calculate the following to the correct number of significant figures.

a) 2

b) 1.5

c) 1.51

d) 1.510

e) 1.5103

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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 × 10^{4}

D) 1.3 × 10^{4}

E) 1.319 × 10^{4}

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How many significant figures are in 1009.630 mL?

A) 3

B) 4

C) 5

D) 6

E) 7

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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

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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

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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

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Perform the following calculation to the right number of sig figs:

a) 1

b) 2

c) 3

d) 4

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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

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