1

Significant Numbers in Calculations

A calculated answer (example density calculations) cannot be more precise than the least precise measuring tool. So, we will record calculated answers to show the uncertainty of the least precise measurement.

2

Adding and Subtracting

Used two different measuring tapes. 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

ALL ABOUT DECIMALS

Rounding

• 5 or higher - round number up

• 4 or lower - number stays the same

• If asked to round to a certain place (tenths, nudreths, etc.), evaluate that number to see if it should stay the same or round up.

4

Learning Check

In each calculation, round the answer to the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 =

1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =

1) 40.725 2) 40.73 3) 40.7

5

Multiplying and Dividing

The answer recorded when numbers are multiplied or divided in science reflects the least precise measuring tool’s number of significant figures.

This is accomplished by rounding numbers (or adding zeros if necessary).

NOT ALL ABOUT DECIMALS

6

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

7

Solution

A. 2.19 X 4.2 = 2) 9.2

B. 4.311 ÷ 0.07 = 3) 60

C. 2.54 X 0.0028 = 2) 11

0.0105 X 0.060

Can your calculator do this?

Continuous calculator operation =

2.54 x 0.0028 0.0105 0.060