Using a Calculator
Number
Round once, at the end
- Values are never rounded partway through a calculation: the full display is carried forward and only the final answer is rounded
- Rounding early shifts the final figure, and the more steps that follow, the larger the shift
- Where a value is needed again later, recall it from the calculator's memory rather than retyping a rounded version
Exam tip
Write the display, then round
When a calculation must be rounded to a stated accuracy, the unrounded value earns a mark of its own, so write 7.754 098… before giving 7.75 to 2 decimal places. If a slip makes your value wrong, rounding it correctly can still earn that mark, but only when the longer value is written down. So copy more figures from the display than the answer needs, then round once.
Worked example
The cost of rounding too early
Work out 2/3 of 285, first exactly and then using 0.67 in place of the fraction. Compare the results.
Solution:
- Keeping the fraction exact: 285 × 2 ÷ 3 = 190
- Replacing 2/3 with the rounded 0.67: 285 × 0.67 = 190.95
- The rounded version is out by almost a whole unit, from a rounding that looked harmless
- Entering the fraction itself, rather than a decimal approximation of it, avoids this entirely
Worked example
Showing a value is correct to a given accuracy
£1600 is invested at 1.8% per year compound interest. Show that its value after 7 years is £1813, correct to the nearest pound.
Solution:
- A 1.8% increase each year is a multiplier of 1.018
- The value after 7 years is 1600 × 1.018⁷ = 1812.818…
- Write the value to more figures than the printed one: £1812.82, which is £1813 to the nearest pound
- Writing only £1813 would show nothing, because that is the value you were given
- Rounding 1.018⁷ = 1.1330… to 1.13 first gives 1600 × 1.13 = £1808, which does not round to £1813, so carry the full display
- If a later part needs this value, start from the printed £1813