Rounding to decimal places and significant figures, estimating calculations using rounding, and finding the upper and lower bounds of measurements, including error intervals and bounds in calculations (Higher tier).

What this dot point is asking

Edexcel expects you to round numbers to decimal places and significant figures, to estimate the answer to a calculation by rounding, and at Higher tier to work with bounds: the largest and smallest a rounded measurement could really be. Estimation is a non-calculator skill that checks whether a calculator answer is sensible, and bounds questions test careful reasoning about accuracy.

Rounding to decimal places and significant figures

Rounding reduces a number to a stated accuracy. The rule is always to look at the digit immediately after the place you are rounding to.

To round $3.14159$ to $2$ decimal places, look at the third decimal ($1$): it is below $5$, so the answer is $3.14$. To round $4736$ to $2$ significant figures, the third significant figure is $3$, so round down and keep the place value with zeros: $4700$. The trailing zeros are needed to keep the number the right size.

Estimating calculations

To estimate, round every number to one significant figure, then do the easier calculation. This gives a quick check on a calculator answer.

For $\dfrac{19.6 \times 4.1}{8.3}$, round to $\dfrac{20 \times 4}{8} = \dfrac{80}{8} = 10$. The exact answer is about $9.68$, so the estimate confirms the order of magnitude. Watch out for dividing by numbers below $1$, which makes the result larger, not smaller.

Error intervals

When a value has been rounded, an error interval states the range it could have come from, using the bounds.

Bounds in calculations (Higher)

When rounded measurements are combined, the result also has bounds. The trick is knowing which bound to use.

So for speed $= \dfrac{\text{distance}}{\text{time}}$ with rounded values, the fastest possible speed uses the largest distance and the smallest time. Reasoning carefully about which extreme makes the answer biggest or smallest is the whole skill here.

A common follow-up asks you to give an answer "to a suitable degree of accuracy". The method is to find both the upper and lower bound of the final calculation, then round to the place where they first agree. If the upper bound of a speed is $7.43\,\text{m/s}$ and the lower bound is $7.38\,\text{m/s}$, the two agree to the nearest whole number ($7$), but not to one decimal place, so a sensible answer is $7\,\text{m/s}$. This shows that the rounding in the original data limits how precisely the answer can be stated, which is the deeper point Edexcel is testing.

Why bounds matter

Every real measurement is rounded, so no measured value is ever exact. Bounds make that uncertainty explicit and let you state the range a true value must lie in. Engineers and scientists use exactly this reasoning to decide whether parts will fit or whether a result is reliable. In the exam, bounds questions reward students who can reason about "best case" and "worst case" rather than just plugging in the rounded figures, which is why they tend to discriminate between grades at the top of the Higher tier.