# 3.13 Significant Figures

## Significant Figures

• Significant figures must be used when dealing with quantitative data
• Significant figures are the digits in a number that are reliable and absolutely necessary to indicate the quantity of that number
• There are some important rules to remember for significant figures
• All non-zero digits are significant
• Zeros between non-zero digits are significant
• 4107 (4.s.f.)
• 29.009 (5.s.f)

• Zeros that come before all non-zero digits are not significant
• 0.00079 (2.s.f.)
• 0.48 (2.s.f.)

• Zeros after non-zero digits within a number without decimals are not significant
• 57,000 (2.s.f)
• 640 (2.s.f)

• Zeros after non-zero digits within a number with decimals are significant
• 689.0023 (7.s.f)

• When rounding to a certain number of significant figures:
• Identify the significant figures within the number using the rules above
• Count from the first significant figure to the specified number
• Use the next number as the ‘rounder decider’
• If the decider is 5 or greater, increase the previous value by 1

#### Worked example

Write 1.0478 to 3 significant figures

Step 1: Identify the significant figures

They are all significant figures

Step 2: Count to the specified number (3rd s.f.)

1.0478

Step 3: Round up or down

1.05 (3 s.f)

#### Exam Tip

An exam question may sometimes specify how many significant figures the answer should be, make sure you keep an eye out for this, as a mark is often given for that! ### Get unlimited access

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