Significant Figures (Edexcel International A Level Physics)

• 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 number of 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)

• Data in tables must also be to the same number of significant figures in each column
• An example of data table with consistent significant figures in the data is:

Example Table With Correct Significant Figures

• In this table, all the data is to 3 s.f.
  • It is important that data in each column must be to the same number of significant figures
• A table of data with inconsistent significant figures would look like:

Example Table With Incorrect Significant Figures

f / Hz	l / m
250.0	0.322
320	0.25
348.23	0.2283
512	0.160

• In the first column, some are to 4 s.f., 3 s.f. and 5 s.f. 
  • These should ideally all be to 3 s.f
• In the second column, some are to 2 s.f., 3 s.f. and 4 s.f.
  • These should ideally all be to 3 s.f.
• When considering how many significant figures to put the data in, the resolution of the instrument must be considered
  • A ruler has a resolution of 1 mm
  • This means all measurements in mm with a ruler, should be recorded to 1 s.f as a more precise value cannot be known due to the limitations of the measuring instrument

• The correct table of results would look like

f / Hz	l / m
250	0.322
320	0.250
348	0.228
512	0.160