Rounding to Decimal Places

Round a decimal to 1, 2 or 3 decimal places by looking at the one digit just after the last place you keep.

In the exam for Cambridge IGCSE Maths 0580, Edexcel IGCSE Maths 4MA1, Cambridge O Level Maths 4024 · 23 real past-paper questions below

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What Decimal Places Are

Decimal places are the digits after the point. 7.2586 has 4 of them. Rounding to 2 decimal places means keeping just 2.

Rule

Count the places you keep after the point. Look at the ONE digit after them. 5 or more: the last kept digit goes up 1. 4 or less: it stays.

Round 7.2586 to	Answer
1 decimal place	7.3
2 decimal places	7.26
3 decimal places	7.259

Key idea

Nearest 10 or 100 is in the Rounding lesson. Here you always count from the decimal point.

Two Decimal Places

The 1-mark question you see most: "Write 4.6371 correct to 2 decimal places."

Worked example

1
$4. 6371$ — Count 2 digits after the point: 6 and 3. These are the digits you keep.
2
$4.63 71$ — Look at the next digit only, the 7. It alone decides whether the 3 changes. Ignore the 1.
3
$7 \geq 5$ — 7 is 5 or more, so the last digit you keep goes up by 1.
4
$4.6 4$ — The 3 becomes 4 and the digits after it are dropped. 4.6371 is nearer 4.64 than 4.63.

Common mistake

Rounding twice from the end: 4.6349 to 4.635, then to 4.64. Look at the 3rd digit once. It is 4, so the answer is 4.63.

Key idea

Keep the zero a carry leaves: 2.3962 becomes 2.40, not 2.4. The 0 shows it has 2 decimal places.

One Decimal Place

The 1-mark question: "Write 38.462 correct to 1 decimal place." Keep 1 digit after the point, and the 2nd one decides.

Worked example

1
$38. 462$ — 1 decimal place means keep 1 digit after the point: the 4.
2
$38.4 62$ — The next digit, the 6, decides. The 2 after it does not matter.
3
$6 \geq 5$ — 6 is 5 or more, so the 4 goes up by 1.
4
$38. 5$ — The 4 becomes 5 and the rest is dropped. 38.462 is nearer 38.5 than 38.4.

A 9 that goes up carries, like counting.

Worked example

1
$9. 96$ — Keep 1 digit after the point: the 9.
2
$9.9 6$ — The next digit is 6. It is 5 or more, so the 9 must go up by 1.
3
$9.9 + 0.1 = 10.0$ — A digit cannot become 10, so it carries, like counting: 9.9 plus one tenth is 10.0.
4
$10. 0$ — Keep the 0 after the point. It shows the answer has 1 decimal place.

Common mistake

Writing 10 for 9.96. The question asks for 1 decimal place, so write 10.0.

Small Numbers: Zeros Count

Exams often ask you to round a small number, like 0.006382, to 3 decimal places. The zeros after the point count as places too.

Worked example

1
$0.006382$ — The question asks for 3 decimal places. Count every digit after the point, zeros included.
2
$0. 006382$ — Keep the first 3 digits after the point: 0, 0 and 6.
3
$0.006 382$ — The 4th digit after the point, the 3, decides.
4
$3 < 5$ — 3 is 4 or less, so the 6 stays as it is.
5
$0.00 6$ — Drop the digits after the 6. The answer has exactly 3 decimal places.

Common mistake

Writing 0.00638. That is 3 significant figures, not 3 decimal places. For decimal places, always count from the point, zeros included.

Key idea

If the last kept digit goes up, the zeros stay: 0.003961 to 3 decimal places is 0.004.

Round a Calculator Answer

The follow-on question: you work something out on a calculator, then "give your answer to 3 decimal places" or to 1 decimal place.

Worked example

1
$\frac{6.2 + 3. 5 ^{2}}{2.4 \times 1.8}$ — The question. Key it in one go, so the calculator divides the whole top by the whole bottom.
2
$= 4.270833333$ — Write down the full display first. In a two-part question this line earns its own mark.
3
$4.270 833333$ — For 3 decimal places, keep 270. The 4th digit, the 8, decides.
4
$\approx 4.27 1$ — 8 is 5 or more, so the 0 goes up to 1.
5
$4.2 70833333$ — For 1 decimal place, go back to the full display. Keep the 2. The 2nd digit, the 7, decides.
6
$\approx 4. 3$ — 7 is 5 or more, so the 2 goes up to 3.

Key idea

Write the whole display before you round. If your display is wrong but you round it correctly, you can still get the rounding mark.

Common mistake

Rounding the 3-place answer again. Always round from the full display, once.

Key idea

How to key the fraction is in the Using a Calculator lesson.

Which Method? Read the Question

The words after "correct to" tell you where to stop.

You see	You do
1 decimal place	keep 1 digit after the point, 2nd decides
2 decimal places	keep 2 digits, 3rd decides
3 decimal places	keep 3 digits, 4th decides
Money, to the nearest cent	2 decimal places: a cent is a hundredth of a dollar
Nearest 10, 100 or whole number	Rounding
3 significant figures	Significant Figures
Write all the figures on the display	Using a Calculator
Smallest value it could have been	Upper and Lower Bounds

Key idea

Check your answer: count the digits after the point. There should be exactly as many as the question asks, zeros included.

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Real past-paper questions on rounding to decimal places

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