Significant FiguresSignificant Figures

Significant figures in a measurement includes all of the digits that are known, plus a last digit that is estimated.

•All measurements are approximations…….•no measuring device can give perfect measurements without experimental uncertainty.

•The numbers reported in a measurement are limited by the measuring tool

Read the bottom of the meniscus

This cylinder is accurate to the ones place = 35 mL

We can see that the meniscus falls right on the line for 35, so we estimate to the tens place = 35.0 mL

Significant figures (sig figs)Significant figures (sig figs)

When we measure something, we When we measure something, we can (and do) always estimate can (and do) always estimate between the smallest marks.between the smallest marks.

21 3 4 5

4.5 cm

Significant figures (sig figs)Significant figures (sig figs)

The better marks the better we can The better marks the better we can estimate.estimate.

Scientist always understand that the Scientist always understand that the last number measured is actually an last number measured is actually an estimate.estimate.

21 3 4 5

4.55 cm

Significant figures (sig figs)Significant figures (sig figs)

The measurements we write down The measurements we write down tells us how accurate the ruler is tells us how accurate the ruler is that we measured withthat we measured with

141 142

142.13cm

Counting Significant Figures

SF?

38.15 cm

5.6 ft

65.6 lb

122.55 m

All non-zero digits are significant.

ANSWERS

4

2

3

5

Counting Significant Figures

Any zero between nonzero digits are significant.

SF?

50.8 mm

2001 mi

0.702 lb

0.00405

ANSWERS

3

4

3

3 THE SANDWICHEDZEROS

Counting Significant Figures

All zeroes to the left of nonzero digits are not significant.

SF?

0.008 mm

0.0156 oz

0.0042 lb

0.000262 mL

ANSWERS

1

3

2

3 PLACEHOLDERS, ONLY

Counting Significant FiguresZeroes to the right of nonzero digits ARE significant if a decimal pt. is

present.

SF?

25.00 in.

0.0200 yr

1.0 gal

ANSWERS

4

3

2

IF THEY WEREN’T SIGNIFICANT THEN WE WOULDN’T WRITE THEM

Zeroes to the right of nonzero digits ARE NOT significant if a decimal pt. is

absent.

Counting Significant Figures

SF?

25,000 in.

200 yr

48,600 gal

ANSWERS

2

1

3

ONLY BEING USED AS PLACE HOLDERS

Adding and Subtracting

The answer has the same number of decimal places as the measurement with the fewest decimal places.

25.2 one decimal place

+ 1.34 two decimal places

26.54

answer 26.5 one decimal place

Multiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Learning Check

A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 =

0.0105 X 0.060

1) 11.3 2) 11 3) 0.041