Significant Figures

Not all numbers matter…

Significant Figures

• Definition: Digits of a number that are relevant when doing mathematical calculation.

• Significant figures are useful so we know when to “cut off” the amount of digits used in answering a problem.

• Just because it’s on the calculator, doesn’t mean it has to be part of the written answer…

Rules for Significant Figures

• Most figures are significant• There are 2 basic rules for when a digit, or

“figure” in a number isn’t significant.

• Rule #1: If a “0” is: a) at the end of a number AND

b) THERE’S NO DECIMAL POINT then those 0’s aren’t significant.

Rule #1- Examples

Some of the digits here are significant and some are not:

240,000

5024

200.300

significant NOT significant

Significant

Significant

Rules for Significant Figures

• Rule #2: If a “0” is at the BEGINNING of a number, it is NOT significant

Rule #2- Examples

Some of the digits here are significant and some are not:

0245.08

0.000005024

NOT significant significant

NOT Significant significant

Practice

• On your white board, write down the number of significant digits for each number, then hold your board up facing the teacher.

Practice

23061

Practice

26,000

Practice

26,000.0

Practice

26,000.030

Practice

03.14

Practice

0.00314

Using Significant Figures

• We use significant figures in math to know how “much answer” to use.

• For Example:

• The number goes on forever, you need to know how many decimal places to use.

666.03

2

Addition and Subtraction

• The answer has the least amount of numbers after the decimal as the numbers you are adding together.

Example

Consider the problem:

100.37 2.356 + 6000.652274

Two places after the decimal

Three places after the decimal

Six places after the decimal

Example

Consider the problem:

100.37 2.356 + 6000.652274 6103.37

Two places after the decimal

Three places after the decimal

Six places after the decimal

Two places after the decimal in the answer.

Multiplication and Division

• The answer matches the smallest number of significant digits as the numbers you are multiplying or dividing together.

Example

• Consider the problem:

120 x 2.28

273.6

Two significant digits

Three significant digits

Needs Two significant digits

Example

• Consider the problem:

120 x 2.28

270

Two significant digits

Three significant digits

Two significant digits

This number gets rounded off and the last digit becomes a 0

Practice

• Complete the worksheet on Significant Figures for your classwork today.