topic 0.4 intro to sig figs

​Why do we need to round this way?

​In science we work with measured values, which are inherently uncertain no matter how sensitive our measuring tools are. Performing calculations with measured values doesn't take the uncertainty away, so we must round our answers to accurately reflect the uncertainty in the measurements.

Multiple Choice

State the number of significant figures in the following measurement: 153.0 mL

• 1

• 2

• 3

• 4

Multiple Choice

State the number of significant figures in the following measurement: 0.012 km

• 1

• 2

• 3

• 4

Multiple Choice

State the number of significant figures in the following measurement:

100000000 s

• 1

• 9

• 10

Multiple Choice

State the number of significant figures in the following measurement:

9009.00 Pa

• 2

• 4

• 5

• 6

Multiple Choice

State the number of significant figures in the following measurement:

0.000008 C

• 1

• 2

• 6

• 7

Multiple Choice

How many significant figures does the following number have? 1.2500 x $$10^3$$  (only concern yourself with the base number!!! the x10 and exponent do not factor in)

• 5
• 3
• Ambiguous: 3 or 5

• 7

Multiple Choice

How many sig figs are there?
100.00

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• 3
• 4
• 5

Multiple Choice

How many sig figs are there?
4004

• 1
• 2
• 3
• 4

Multiple Choice

How many sig figs are there?
0.00400

• 1
• 3
• 5
• 6

Multiple Choice

What is the value 7873.5, rounded to 3 sig figs?

• 7870

• 787

• 7870.0

• 7870.

​Manipulating Significant Figures

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Addition or Subtraction –

When adding or subtracting measurements with decimals, the answer must have the same number of decimals (digits to the right of the decimal point) as there are in the measurement having the fewest decimals.

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Ex., 25.1 g + 2.03 g = 27.13 g (this is what a calculator would display)

The proper way to represent the answer is 27.1 g because the measure of 25.1 g has the fewest decimals (one).

​Manipulating Significant Figures

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Multiplication and Division –

For multiplication and division, the answer can have no more significant figures than are in the measurement with the fewest significant figures.

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Ex., 3.050 g / 8.47 mL = 0.360094451 g/mL, (this is what a calculator would display)

The proper way to represent the answer is 0.360 g/mL because the measure of 8.47 mL has the fewest sig figs (three), and 0.360 has three sig figs.

Multiple Choice

$$7.80\div0.091=\ ?$$  
Round your answer to the correct number of sig figs.

• 85.71429

• 85.71

• 85.7

• 86

Multiple Choice

3.11 x 2.1 =

• 6.531

• 6.53

• 6.5

• 7

• 6

Multiple Choice

Select the answer reported to the correct number of significant figures.

85 X 973

• 82705

• 83

• 82700

• 83000

Multiple Choice

Select the answer reported to the correct number of significant figures. $$930\div412$$  

• 2.2

• 2.26

• 2.25

• 2.3

Multiple Choice

$$\left(125+2.48\right)\div\left(23.75-21.0\right)\ =\ ?$$  

• 50

• 46.36

• 46

• 46.4