Measures and accuracy: round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures)

The idea

Rounding changes a value to a nearby, simpler value while keeping it close enough for the context. To round to a given number of decimal places, find the required decimal position, then inspect the next digit: if it is 5 or more, increase the required digit by 1; otherwise leave it. For significant figures, start counting from the first non-zero digit; round at the required significant figure using the following digit. Measures may be rounded to a sensible unit, such as 3.7 m to the nearest metre, or 0.0482 kg to 2 significant figures, giving 0.048 kg. Always state the degree of accuracy and check that the rounded value is reasonable in context.

What earns the marks

• Identify the required place value or significant figure position before rounding.
• Use the digit immediately after the required position to decide whether to round up or keep the digit.
• Round up when the deciding digit is 5 or more; otherwise keep the required digit unchanged.
• For significant figures, count from the first non-zero digit, not from the decimal point.
• Preserve trailing zeros where they are needed to show the stated degree of accuracy.
• Check that the rounded measure is sensible for its context and unit.

Common mistakes and how to put them right

• Counting significant figures from the decimal point rather than from the first non-zero digit.

  Put it right by starting at the first non-zero digit and counting every digit after it.

• Dropping a trailing zero that is needed to show the required accuracy.

  Put it right by keeping zeros that hold the stated place value, for example 4.60 to 2 decimal places.

• Rounding a value such as 0.0496 to 2 significant figures as 0.04 instead of 0.050.

  Put it right by counting from the 4 and rounding the 9 up, which changes the earlier digit.

• Applying rounding repeatedly to intermediate values in a multi-step calculation.

  Put it right by keeping full accuracy until the final answer, then rounding once.

Exam tips

• Underline the digit at the required place or significant figure before deciding, so you do not round the wrong position.
• Write the degree of accuracy next to your answer, for example 3.7 m (1 d.p.) or 0.048 kg (2 s.f.), to show what you have done.
• For measures, check the unit and whether the rounded value is realistic; a length of 3.7 m to the nearest metre is 4 m, not 3 m.