Significant Figures

Measured Numbers

When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

Exact Numbers

Obtained when you count objects2 soccer balls

1 watch

4 pizzasObtained from a defined relationship

1 foot = 12 inches

1 meters = 100 cmNot obtained with measuring tools

Exact numbers are obtained by

1. Counting

2. Definition

3. Measuring

4. Counting & Definition

Measured numbers are obtained by

1. Measuring

2. Counting

3. Definition

Classify as exact or measured number : Gold melts at 1064

Celsius.1. Exact

2. Measured

Classify as exact or measured: 1 yard = 3 feet

1. Exact

2. Measured

Classify as exact or measured:A red blood cell with diameter 6 x

10 -4cm.1. Exact

2. Measured

Classify as exact or measured: There were six hats on the shelf.

1. Exact

2. Measured

Classify as exact or measured:A can of soda contains 355 mL of

soda. 1. Exact

2. Measured

Uncertainty in Measurement

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

Significant figures in a measurement include the known digits plus one estimated, or uncertain digit

This nail is 6.3 centimeters long for sure, but what exactly

is the value of the hundredths place

– 6.35, 6.36, 6.37?

“Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.”

In the nail example, the hundredths place (3.36, the 6) is uncertain, or estimated.

A SIGNIFICANT FIGURE IS NOT ALWAYS CERTAIN – THE LAST DIGIT OF ANY MEASUREMENT IS ESTIMATED!!!

Rules For Significant Figures

1) All non-zero digits are significant

Examples:

35 2 significant figures

48.96 4 significant figures

How many significant figures in 896.76

A. 2

B. 3

C. 4

D. 5

Rules For Significant Figures

2) Zeros between numbers (sandwiched zeros) are all significant

Example:

304 – 3 significant digits

56.098 – 5 significant digits

How many significant figures in 1,043?

A. 1

B. 2

C. 3

D. 4

Rules For Significant Figures

3) Any zero appearing in front of a non-zero digit is NOT significant (regardless of a decimal)

Example:

0.876 – 3 significant digits

0.0056 – 2 significant digits

How many significant figures in 0.0008

A. 1

B. 3

C. 4

D. 5

Rules for significant figures

4) Zeros at the end of a number AND to the right of a decimal point are significant

Examples:

72.00 – 4 significant figures

7.000000000 – 10 significant figures

How many significant figures in 5.6000

A. 2

B. 4

C. 5

D. Help, I’m confused!

Rules For Significant Figures

5. A) Zeros at the end of the number WITHOUT a decimal place are NOT significant.

Example:

3,000 – 1 significant figure

560 – 2 significant figures

How many significant figures does 453,000 have?

A. 2

B. 3

C. 4

D. 6

Rules For Significant Figures

5 B) Zeros at the end of a number to the LEFT of a decimal point are significant

Example:

300.- Has three significant figures

4,000. – Has four significant figures

How many significant figures does 1,000. have?

A. 1

B. 2

C. 3

D. 4

How many sig figs does 305.00 have?

A. 2

B. 3

C. 5

D. Help! I’m confused!

How many sig figs does 0.009 have?

A. 1

B. 2

C. 3

D. 4

How many sig figs does 5,600.

A. 1

B. 2

C. 3

D. 4

Sig Figs in Calculations

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from 1) adding or subtracting

2) multiplying or dividing

Sig Figs and Addition/Subtraction

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

Round the answer to the correct number of significant

figures235.05 + 19.6 + 2.1 =

A) 256.75

B) 256.8

C) 257

Round the answer to the correct number of significant

figures 58.925 - 18.2

A) 40.725

B) 40.73

C) 40.7

Multiplying and Dividing with Sig Figs

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.

2.19 X 4.2

A. 9

B. 9.2

C. 9.198

4.311 ÷ 0.07

A. 61.58

B. 62

C. 60