01 — Explanation
When should I round during a multi-step calculation?
Never round in the middle. Keep the full, unrounded value on your calculator throughout (using the ANS key or memory), and round only the final answer.
Cambridge's default rounding conventions (unless the question says otherwise):
- Non-exact numerical answers → 3 significant figures.
- Angles → 1 decimal place.
Common Slip
writing down a rounded value after each stage of a multi-step calculation. This accumulates rounding error and can shift the final answer outside the accepted range.
02 — Explanation
How do I enter a complicated fraction or root correctly?
Without brackets, a calculator only divides by the first term after the division sign. Always enclose a multi-term numerator or denominator in brackets.
Example: calculate , to 3 significant figures.
- Enter as
(6.4^2 - 3.9) ÷ √(2.5 + 1.3), with brackets around both the numerator and the contents of the root. - Read the full display:
- Round only at the end: (3 s.f.).
03 — Explanation
How do I interpret unusual calculator displays?
A calculator doesn't know it's showing money or time — you have to translate the display yourself.
| Calculator shows | Correct interpretation |
|---|---|
4.8 in a money context | \4.80$ |
3.25 in a time context | hours minutes |
2.5 when entering "2 hours 30 min" | Enter as (or use the DMS button) |
Example: a calculator shows after dividing hours worked by days. To convert to hours and minutes: the whole number () is the hours, and the decimal () must be multiplied by to give minutes: . So the answer is hours minutes.
Common Slip
reading as "3 hours 40 minutes" directly. The decimal part is a fraction of an hour, not minutes — it must be multiplied by first.
04 — Explanation
How do I correctly enter a negative number for a calculation like (-5)^2?
Calculators have two different-looking minus symbols: a small (-) button for typing a negative number, and the longer − subtraction button. Using the wrong one can silently change your answer.
Example: find using a calculator.
- Enter the first term as
( (-) 5 ) ^ 2— using the negative-number button, with brackets around the whole base — giving . - Enter the second term as
( (-) 2 ) ^ 3, giving . - Combine using ordinary subtraction:
25 − (−8)= .
Common Slip
typing -5^2 without brackets. Most calculators read this as "take , square it, then make the result negative," giving instead of the intended . Always wrap a negative base in brackets before applying a power.
05 — Common mistakes
Common mistakes to avoid
- Rounding at each intermediate step instead of carrying the exact value through to the end.
- Reading a decimal time display as minutes directly, without multiplying the decimal part by .
- Omitting brackets around a multi-term numerator or denominator, which silently changes what the calculator actually computes.