Topics › KS3 › Number

Rounding & estimation

rnd-01 Present from here

Round $6.248$ to $1$ decimal place.

Option A: $6.25$

Option B: $6$

Option C: $6.3$

Option D: $6.2$

Answer and misconceptions

Option A: $6.25$ ✗
Rounds to 2 decimal places instead of 1Confuses 1 d.p. with 2 d.p.

Option B: $6$ ✗
Rounds to the nearest whole numberThinks "1 decimal place" means round to the units.

Option C: $6.3$ ✗
Rounds in steps from the last digitDoes 6.248 → 6.25 → 6.3; only the hundredths digit (4) should decide.

Option D: $6.2$ ✓ Correct
rnd-02 Present from here

Round $4862$ to the nearest hundred.

Option A: $4800$

Option B: $49$

Option C: $4900$

Option D: $5000$

Answer and misconceptions

Option A: $4800$ ✗
Always rounds down (truncates)Cuts off the tens and units without checking the tens digit.

Option B: $49$ ✗
Drops digits instead of replacing them with zerosLoses place value: 4862 is about 49 hundreds, not 49.

Option C: $4900$ ✓ Correct

Option D: $5000$ ✗
Rounds to the nearest thousand insteadConfuses the hundreds place with the thousands place.
rnd-03 Present from here

Round $0.04073$ to $2$ significant figures.

Option A: $0.04$

Option B: $0.041$

Option C: $0.0407$

Option D: $0.040$

Answer and misconceptions

Option A: $0.04$ ✗
Rounds to 2 decimal places insteadCounts places after the point rather than from the first non-zero digit.

Option B: $0.041$ ✓ Correct

Option C: $0.0407$ ✗
Does not count a zero between non-zero digitsCounts 4 and 7 as the 2 s.f., skipping the 0 in between.

Option D: $0.040$ ✗
Truncates instead of roundingCuts off after the second significant figure without looking at the next digit (7), so does not round up.
rnd-04 Present from here

Which is the best estimate for $49.6 \times 0.52$?

Option A: $25$

Option B: $50$

Option C: $0$

Option D: $250$

Answer and misconceptions

Option A: $25$ ✓ Correct

Option B: $50$ ✗
Rounds 0.52 to the nearest whole numberHas rounded 0.52 to 1; round each number to 1 s.f. (0.5).

Option C: $0$ ✗
Truncates 0.52 to 0Removes the decimal part, so the estimate becomes 50 × 0.

Option D: $250$ ✗
Ignores the decimal point in 0.52Has used 5 instead of 0.5.
rnd-05 Present from here

A pencil is $7$ cm long, to the nearest cm. What is the shortest it could be?

Option A: $6.49$ cm

Option B: $6.5$ cm

Option C: $6$ cm

Option D: $6.95$ cm

Answer and misconceptions

Option A: $6.49$ cm ✗
Thinks the lower bound itself is excluded6.5 rounds up to 7, so 6.5 is the lower bound; 6.49 rounds to 6.

Option B: $6.5$ cm ✓ Correct

Option C: $6$ cm ✗
Subtracts a whole unit for the lower boundThinks "to the nearest cm" means ±1 cm.

Option D: $6.95$ cm ✗
Uses half of 0.1 instead of half of 1Has subtracted 0.05; the bound is half a unit (0.5 cm) below.