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.
666.032
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.