KS3MAT4 · Accuracy, estimation and measures | KS3 Maths

Revise the key ideas

Nearest place — To round 6.748 to two decimal places, look at the third decimal digit: 8 rounds the hundredths up, giving 6.75. To one decimal place it is 6.7 because the next digit is 4.
Significant figures — Start counting from the first non-zero digit: 0.004867 to two significant figures is 0.0049; 48,670 to two significant figures is 49,000. Zeros before the first non-zero digit only locate place value.
Appropriate accuracy — A room length measured to the nearest centimetre does not justify a quoted length to many decimal places. Keep unrounded intermediate values and round the final answer as requested.

Estimate a calculation — For 19.8 × 4.91 ÷ 0.203, round to 20 × 5 ÷ 0.2 = 500. The estimate checks order of magnitude; it is not the accurate answer. Use ≈ for approximately equal.
Bounds from rounding — A positive length given as 8.4 cm to the nearest 0.1 cm lies in 8.35 ≤ L < 8.45 under the usual school convention. The lower endpoint rounds up to 8.4; the upper rounds to 8.5.
Rounding to the nearest tenth. Original illustrative model. Full-size diagram
Possible error — If a positive mass is 12 g to the nearest gram, its absolute rounding error is at most 0.5 g under the stated convention. The true mass is 11.5 ≤ m < 12.5. This uses the school rule that a halfway value rounds up: 11.5 rounds to 12, while 12.5 rounds to 13. A tie convention is a rule for these exactly halfway cases; state it if a different rule is used.
Combining bounds — Two positive lengths rounded to 5 cm and 8 cm have ranges 4.5 ≤ a < 5.5 and 7.5 ≤ b < 8.5. Their sum satisfies 12 ≤ a + b < 14. For a difference, the largest subtraction uses the largest first value and smallest second.
Checking a result — An estimate of £70 cannot support a calculator answer of £700 without rechecking. Test the sign, magnitude, unit and context. Checking by a genuinely different method is stronger than repeating the same key sequence.

Length and mass — 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm; 1 kg = 1000 g and 1 tonne = 1000 kg. Thus 2.35 kg = 2350 g. A smaller unit gives a larger numerical count for the same quantity.
Time — 1 hour = 60 minutes and 1 minute = 60 seconds. Thus 1.5 h = 90 min, while 1 h 50 min = 110 min, not 1.50 h. Time conversion is not decimal place shifting.
Money — £1 = 100p. Convert before combining: £2.40 + 85p = £3.25. State a currency, use two decimal places for ordinary cash amounts and interpret discounts or fares in context.
Area and volume units — Since 1 m = 100 cm, 1 m² = 100² = 10,000 cm² and 1 m³ = 100³ = 1,000,000 cm³. For area, convert both length and width, so multiply by 100 twice. For volume, convert length, width and height, so multiply by 100 three times.
Capacity — 1 litre = 1000 ml = 1000 cm³; 1 ml = 1 cm³; 1 m³ = 1000 litres. Capacity and volume measure three-dimensional space, though containers may have a smaller usable capacity than their exterior volume.
Reading scales — Count intervals, not marks: five equal intervals between 2 and 3 represent 0.2 each. Read the correct unit. An instrument's resolution is the smallest change its scale can show. Record only the accuracy the scale supports; do not add extra decimal places that you could not read.

Multi-step quantities — A 2.4 m board is cut into 35 cm pieces. Convert to 240 cm; 240 ÷ 35 = 6 remainder 30, so six full pieces fit if cutting waste is ignored. A real model may need a saw-width allowance.
Communicating uncertainty — Write measured or rounded values with their accuracy, such as 3.2 m to the nearest 0.1 m. Distinguish exact counts from approximate measurements; a headcount of 32 is not automatically a rounded measure.

50 questions · Random sets of 10. These quick checks support revision; practise longer explanations and justified judgements too.