Significant Figures(Math Skills)

What are they?

Why use them?

How to use them.

Significant Figures – What are they?(Sometimes called significant digits.)

Because the precision of all measuring devices is limited, the number of digits that are valid for any measurement is also limited.

The valid digits in a measurement are called the significant figures.

Why use significant figures?

• They are used in an organized way to round up answers to calculations so that the answer isn’t more precise than the original measurements.

• Example: if you measured the dimensions a box to the nearest whole cm you would not list the calculated volume to the nearest 0.01 cm3.

• You would round it to the nearest whole cm3.

• Thus, the driving force behind significant digits is the precise reporting of experimentally measured data.

• You do not want your calculated figures to be more precise than the original measurements.

Rules for determining significant digits

1. Any nonzero digit is significant.

2. Any zero sandwiched between two other significant figures is significant.

12 (2) 342 (3)

205 (3)

380.5 (4)

56003

50.06

(5)

(4)

3. A zero to the right of a nonzero digit but left of the decimal is significant.

980. (3) 980 (2)

What is the difference?

4. A zero to the left of the number is not significant.

0123 (3) 0.065 (2) .000426 (3)

The decimal

5. A zero to the right of a nonzero number and right of the decimal is significant.

13.40 (4) 0.0470 (3) .11600 (5)

Using Sig. Digits in Multiplication and Division

• Round up the answer to a multiplication or division problem so that it has the same number of significant digits as the number with the least number of significant digits in the problem.

Example 1: 10 x 67 =

670 = 700(1) (2) (1)

What happens if there is a 5?• Do you always round up?• There is an arbitrary rule: • If the number before the 5 is odd, round up. • If the number before the 5 is even, round down

The justification for this is that in the course of a series of many calculations, any rounding errors will be averaged out.

350 = 400(1) (2) (1)

Example 1: 10 x 35 =

Odd, so round up

Example 2: 10. x 55 =

Keep at 2 significant digits

Example 3: 749.7 7.0 =

Round up to 2 significant digits

(2) (2)550

107.1 = 110(4) (2) (4) (2)

Addition and Subtraction,a Different Story

• Counting numbers of significant digits are NOT used with addition and subtraction to round up answers to problems.

• Instead you round up according to the least precise of the original measurements or numbers.

Example 1:

12.31 + 10.2 + 8 =

Round up to the one’s place

Example 2:

0.030 + 1.01 + 0.234 =

Round up to the hundredth’s place

30.51 = 31

1.247 = 1.25

Example 3:

58.34 – 22.1 =

Round up to the tenth’s place

36.24 = 36.2