Decimals & Rounding (Years 6–10) — Maths

Round to decimal places and significant figures; convert between fractions and decimals.

A sat-nav says "arriving in about 20 minutes", a news report says "roughly 30,000 fans", a shop rounds your bill to the nearest penny. We round numbers to make them simpler when we don't need every digit — like saying a journey is "about 50 miles" rather than 48.7. The skill is knowing which digit to keep, and whether to round it up or down.

Why this matters: rounding lets you give sensible, readable answers and — just as importantly — estimate what an answer should be so you catch calculator slips. Money, measurements, and science data are almost never quoted to full precision, so this is a life skill as much as an exam skill.

3.7482 is past the halfway point → it rounds up to 3.75

Rounding — the one rule

Look at the digit just after the place you're rounding to. If it's 5 or more, round up; if it's 4 or less, round down (leave it as it is).

That single rule covers rounding to the nearest ten, hundred, thousand, decimal place, or significant figure — only the "place you're rounding to" changes.

Decimal places (d.p.)

"2 decimal places" means keep two digits after the point. It is like trimming a plank to length — you decide where to cut, then check the offcut to see whether the last kept digit nudges up.

3.7482 to 2 d.p.: keep 3.74, then look at the next digit (8). 8 ≥ 5, so round up → 3.75.

Significant figures (s.f.)

Leading zeros are just placeholders. Counting from the first non-zero digit, 0.00408 to 2 s.f. is 0.0041.

Significant figures count from the first non-zero digit. They're handy for very big or very small numbers, where the leading zeros are just placeholders and don't count.

0.00408 to 2 s.f.: the first two significant figures are 4 and 0 (the zeros before the 4 don't count); the next digit is 8, so round up → 0.0041.

Number	Rounded to	Answer
3.7482	2 d.p.	3.75
24.681	1 d.p.	24.7
0.00408	2 s.f.	0.0041
28,500	1 s.f.	30,000

Common mistake: rounding can roll over. 4.98 to 1 d.p. → the 8 rounds the 9 up, which carries again, giving 5.0, not 4.10. Treat the carry like normal addition and it behaves.

Estimating

4.98 sits past halfway, so the carry rolls the 9 over: to 1 d.p. it becomes 5.0, not 4.10.

To estimate an answer quickly, round every number to 1 significant figure and then calculate. It won't be exact, but it tells you roughly what to expect — your reality-check that the calculator answer is in the right ballpark.

31.6 × 4.9 ≈ 30 × 5 = 150. If your calculator ever showed 15 or 1500, you'd know a decimal point had slipped.

Turning fractions into decimals

A fraction is a division: 7 out of 8 shaded means 7 ÷ 8 = 0.875.

A fraction is a division in disguise, so to make it a decimal, divide the top by the bottom. Going the other way, a decimal like 0.35 is 35 hundredths → 35/100 → simplify to 7/20.

7/8 = 7 ÷ 8 = 0.875.

Memory hook: find the rounding place, peek at the next digit, and use "5 or more rounds up". Estimate with 1 s.f. to sense-check every answer.