Number - Measures and accuracy: round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

The idea

Decimal places are counted after the point, while significant figures are counted from the first non-zero digit, so 0.00408 to two significant figures is 0.0041 and the zeros at the front never count. Look at the digit immediately after the place you are keeping: five or more rounds the kept digit up, four or less leaves it alone. An appropriate degree of accuracy usually matches the data you were given, and money is written to two decimal places. An error interval names every true value a rounded figure could have come from. A length recorded as 8.3 cm to one decimal place can be half of 0.1 either side, so 8.25 ≤ x < 8.35, and the upper end stays strict because 8.35 would round up instead. Truncation chops the digits rather than rounding them, so a truncated 8.3 cm gives 8.3 ≤ x < 8.4.

What earns the marks

• The value rounded to the accuracy named in the question, with trailing zeros kept where they carry place value.
• The lower limit of an error interval and one for the upper limit, whichever way round they are written.
• The correct inequality signs, strict at the upper end for a rounded value.
• Treating a truncated value as running from the stated value up to the next one, rather than half a unit either side.

Common mistakes and how to put them right

• Counting the zeros after the decimal point as significant, so rounding 0.00408 to 0.00 and calling it two significant figures.

• Rounding twice, taking 4.4649 to 4.465 and then to 4.47 when two decimal places were asked for.

• Writing an error interval with the same sign at both ends, which wrongly allows 8.35 as a value that rounds to 8.3.

• Using half a unit either side for a truncated measurement, when truncation runs only upwards from the stated value.

Exam tips

• Underline whether the question says decimal places or significant figures before you round anything.
• For an error interval from a rounded value, write the stated value in the middle first and then add and subtract half the rounding unit; for a truncated value, run the interval from the stated value up to the next one.
• Keep full accuracy in the calculator through a multi step question and round only the final answer.