Rounding & Estimation

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Cambridge (CIE) IGCSE — International Maths (Extended)

Rounding & Estimation

Big idea: Rounding means swapping an awkward number for a "nice enough" one by looking at the very next digit — and estimation just means rounding before you calculate, so you can spot silly mistakes and handle messy real-world numbers sensibly.

Summary — everything in this chapter

Rounding to a given place value (nearest 10, 100, 1000...) — look at the digit to the right, decide up or down.
Rounding to a given number of decimal places (d.p.) — same idea, but counting after the decimal point.
Rounding to a given number of significant figures (s.f.) — counting digits from the first non-zero digit.
Knowing what degree of accuracy to use when a question doesn't tell you (hint: 3 s.f. is the default).
Deciding whether to round up or down in real-life "context" problems, even when the maths says otherwise.
Estimating a calculation by rounding every number to 1 significant figure first.
Working out whether an estimate is an overestimate or underestimate.

1. Rounding to a place value or decimal place

Think of rounding like deciding whether to round a price up or down at the till. You look at exactly one digit — the digit immediately to the right of where you're rounding to — and that single digit makes the whole decision. Nothing else matters.

The method, step by step

The Golden Rule of Rounding

Step 1: Find (underline or circle in your head) the digit in the place value you're rounding to.
Step 2: Look at the digit immediately to its right — this is your "decider" digit.
Step 3: If the decider is 5 or more → round UP (the target digit increases by 1).
Step 4: If the decider is less than 5 → round DOWN (the target digit stays the same).
Step 5: Everything after the decider digit gets chopped off or replaced with zeros, depending on whether you're before or after the decimal point.

Here's the part that trips people up: what happens to the "leftover" digits depends on which side of the decimal point you're on.

Rounding to...	What happens to leftover digits	Example
A whole-number place value (10, 100, 1000...)	Fill with zeros up to the decimal point — you need them to keep the number's size correct	1567.45 → nearest 100 → 1600
A number of decimal places	Delete everything after the required decimal place — but you must still show the exact number of d.p. asked for (pad with a trailing zero if needed)	2.395 → 2 d.p. → 2.40 (not 2.4!)

Why does 2.40 need that zero? Writing "2.4" only tells someone you rounded to 1 d.p. Writing "2.40" proves you rounded to 2 d.p. The trailing zero isn't decoration — it's evidence of the accuracy you used. Examiners specifically check for it.

Worked Example — round to 2 decimal places

(i) 345.254

The 2nd decimal place is 5. The decider digit (3rd d.p.) is 4.

4 is less than 5 → round down → the 5 stays a 5.

(ii) 0.295631

The 2nd decimal place is 9. The decider digit is 5.

5 rounds up → the 9 becomes a 10, which carries over: 0.29 → 0.30.

(iii) 4.998

The 2nd decimal place is 9. The decider digit is 8.

8 rounds up → the whole 4.99 carries all the way up to 5.00.

Watch the carry! In example (iii), 4.998 doesn't round to "4.9(10)" — that's not a real number. The extra 1 carries into the next column, and the next, until it settles: 4.998 → 5.00. This "chain reaction" happens whenever you round up a string of 9s. Don't panic — just carry the 1 as far as it needs to go.

Practice Question 1

Round 6.5049 to (a) the nearest whole number, (b) 2 decimal places, (c) 3 decimal places.

Practice Question 2

Round 2 530 457 to the nearest 1000, and explain in words what the answer means.

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Also in the full note

2. Rounding to significant figures (s.f.)
3. Choosing the right degree of accuracy
4. When to round up or down in real life
5. Estimating a calculation
6. Overestimate or underestimate?
What to Memorise
Concepts Checklist
Exam Tips & Common Mistakes

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Rounding & Estimation

Rounding & Estimation

Summary — everything in this chapter

1. Rounding to a place value or decimal place

The method, step by step

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