3.13 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

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)