0580

Rounding, Estimation and Bounds

Number

Finding the first significant figure

  • Reading left to right, the first significant figure is the first non-zero digit
    • In 5081 it is the 5
    • In 0.00407 it is the 4
  • Zeros in front of that digit only position the number and are never significant
  • Zeros sitting between non-zero digits are significant, because they carry information
    • The second significant figure of 5081 is the 0

Rounding and padding

  • Count rightwards to the required figure, then apply the usual rounding rule
  • Large numbers are padded with zeros out to the decimal point
    • 5081 to two significant figures is 5100
  • For a decimal, zeros fill the gap from the point up to where the significant figures begin
    • 0.00407 to two significant figures is 0.0041
Exam tip

Every calculator paper — all 21 of Papers 3 and 4 — prints the same default: "correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question." Round only at the very end, and a requested number of decimal places includes a final zero, so 0.50 is right where 0.5 is not.

Worked example

Rounding to significant figures

Write 0.004 078 2 to 3 significant figures, and 46 851 to 2 significant figures.

Solution:

  • The first significant figure is the first non-zero digit, so leading zeros never count
  • In 0.004 078 2 the first significant figure is the 4, the second is the 0 after it, and the third is the 7
  • The next digit is 8, which is 5 or more, so the 7 rounds up to 8
  • 0.004 078 2 = 0.004 08 to 3 significant figures
  • In 46 851 the first two significant figures are 4 and 6
  • The next digit is 8, so the 6 rounds up to 7
  • The place holders must stay, so the answer is 47 000, not 47