MathematicsExam code: 0580
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
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