Round to decimal places and significant figures, estimate calculations by rounding to one significant figure, and find upper and lower bounds and use them in calculations (Higher tier).

What this dot point is asking

WJEC asks you to round numbers to a given number of decimal places or significant figures, to estimate the answer to a calculation by rounding, and at Higher tier to find the upper and lower bounds of a measurement and use those bounds in calculations. Rounding controls how you present answers throughout the course; estimation is a quick sanity check; and bounds capture the unavoidable uncertainty in any real measurement. The bounds work, in particular, is a reliable source of Higher-tier marks.

Rounding to decimal places and significant figures

Both methods follow the same rule: look at the digit immediately after the place you are keeping, and round up if it is $5$ or more.

For decimal places, count digits after the point: $3.748$ to $2$ decimal places is $3.75$, because the third decimal $8$ rounds the $4$ up.

Estimating calculations

An estimate gives a quick check that a calculator answer is the right size.

Round every number in the calculation to one significant figure, then work out the simplified version. This catches gross errors such as a misplaced decimal point. Dividing by a number less than $1$ makes the result larger, which is the part students most often get wrong: $\tfrac{1}{0.2}$ is $5$, not a fraction.

Upper and lower bounds (Higher)

Every measured value is rounded, so the true value lies in a range.

When bounds are combined in a calculation, choose them to make the result as large or as small as required.

The key insight is that for a quotient, a larger numerator increases the result while a larger denominator decreases it, so you pick opposite extremes.

Choosing bounds for products and sums

The rule for which bound to pick depends on the operation. For a product, the largest result uses both upper bounds and the smallest uses both lower bounds, because multiplying two larger numbers gives a larger answer. For a sum, again both upper bounds give the maximum. For a difference $a - b$, the largest result uses the upper bound of $a$ and the lower bound of $b$, since subtracting a smaller number leaves more. Sketching the four corner combinations is a safe way to be sure, but the underlying logic is always: make the quantity that increases the result as big as possible and the quantity that decreases it as small as possible.

Truncation and degree of accuracy

Sometimes a value is truncated (cut off) rather than rounded; a length truncated to $7$ cm could be anything from $7$ up to just under $8$ cm, so its bounds are not symmetric. WJEC also asks you to state a calculated answer "to an appropriate degree of accuracy". A neat way to decide is to compute both bounds of the final answer and round to the figures on which they agree: if the upper and lower bounds for a speed are $9.50$ and $9.48$ m/s, they agree to two significant figures, so $9.5$ m/s is a sensible, justified degree of accuracy. This links bounds back to the rounding skills at the start of the topic.

Why this matters

Rounding decides how every answer in the course is presented, and getting significant figures right is a frequent easy mark. Estimation guards against calculator slips on Unit 2. Bounds connect to area and volume, speed and density, and any measured quantity, and they reward careful reasoning about which extreme to use, exactly the kind of AO3 thinking WJEC values at Higher.