Chapter 2:Fractions, Decimals and Percentages, 2.1:Rounding Numbers

What is rounding?

  • Rounding changes a number to a simpler value that is close to the original number.

  • The rounded number is an approximation, not usually the exact value.

  • Rounding makes numbers easier to read, compare and calculate with.

Rounding to the nearest whole number

  • Look at the tenths digit.

  • If the tenths digit is 5 or more, round the whole-number digit up.

  • If the tenths digit is 4 or less, keep the whole-number digit the same.

  • Remove the decimal part.

Examples:

  • 7.3 → 7

  • 7.8 → 8

  • 12.5 → 13

  • 19.42 → 19

Rounding to decimal places

  • Decimal places are the digits after the decimal point.

  • To round to 1 decimal place (1 d.p.), look at the second decimal digit.

  • To round to 2 decimal places (2 d.p.), look at the third decimal digit.

  • To round to 3 decimal places (3 d.p.), look at the fourth decimal digit.

  • If the next digit is 5 or more, increase the last digit by 1.

  • If the next digit is 4 or less, leave the last digit unchanged.

Examples:

  • 4.67 to 1 d.p. = 4.7

  • 4.63 to 1 d.p. = 4.6

  • 8.246 to 2 d.p. = 8.25

  • 8.243 to 2 d.p. = 8.24

Rounding to significant figures

  • Significant figures count the important digits starting from the first non-zero digit.

  • To round to 1 significant figure, keep the first non-zero digit.

  • To round to 2 significant figures, keep the first two significant digits.

  • Look at the digit immediately after the last significant figure.

  • If it is 5 or more, round up.

  • If it is 4 or less, leave the last significant figure unchanged.

Examples:

  • 47 to 1 s.f. = 50

  • 43 to 1 s.f. = 40

  • 362 to 2 s.f. = 360

  • 3,847 to 2 s.f. = 3,800

  • 0.00476 to 2 s.f. = 0.0048

Decimal places vs significant figures

  • Decimal places count digits after the decimal point.

  • Significant figures count important digits starting from the first non-zero digit.

  • Zeros at the beginning of a decimal number are not significant figures.

  • Example: 0.00452 has 3 significant figures but 5 decimal places.

Rounding with zeros

  • Zeros can be important when showing significant figures.

  • 4,500 could represent different levels of accuracy depending on the context.

  • Writing numbers in standard form can make the number of significant figures clear.

  • Example: 4.5 × 10³ has 2 significant figures.

Rounding and accuracy

  • The more decimal places or significant figures given, the more precise a rounded value is.

  • Rounding too early in a calculation can make the final answer less accurate.

  • When doing multi-step calculations, keep extra digits during the calculation and round the final answer when appropriate.

Estimating

  • Rounding can be used to estimate an answer quickly.

  • Numbers are rounded to convenient values before calculating.

  • An estimate should be close to the exact answer but does not need to be exact.

Example:

  • 49.7 × 21.2

  • Estimate: 50 × 20 = 1,000

  • So the exact answer should be around 1,000.