Rounding & Estimation (Edexcel IGCSE Maths A (Modular))
Revision Note
Written by: Naomi C
Reviewed by: Dan Finlay
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Rounding & Estimation
How do I round a number to a given place value?
Identify the digit in the required place value
Circle the number to the right of the required place value
If the circled number is 5 or more then you round to the bigger number
If the circled number is less than 5 then you round to the smaller number
Put a zero in any following place values before the decimal point
E.g. 1567.45 to the nearest 100 would be 1600
How do I round a number to a given decimal place?
Identify the position of the decimal place you are rounding to
Circle the number to the right of the required decimal place
If the circled number is 5 or more then you round to the bigger number
If the circled number is less than 5 then you round to the smaller number
E.g. 2.435123 to the nearest 2 d.p. would be 2.44
When rounding to decimal places make sure you leave your answer with the required amount of decimal places
Do not put any zeros after the position of the decimal place you are rounding to
E.g. 1267 to the nearest 100 is 1300
But 1.267 to two decimal places (nearest 100th) is 1.27 not 1.270
If asked for a certain number of decimal places, you must give an answer with that number of decimal places
E.g. 2.395 to two decimal places is 2.40 (do not write 2.4)
Worked Example
Round the following numbers to 2 decimal places.
(i) 345.254
(ii) 0.295 631
(iii) 4.998
(i) Identify the second decimal place (5)
Circle the digit to the right of the second decimal place (4)
As this digit is less than 5 we will round the number down
345.25 (2 d.p.)
No zeros are required after the second decimal place
(ii) Identify the second decimal place (9)
Circle the digit to the right of the second decimal place (5)
As this digit is greater than or equal to 5 we will round the number up
0.30 (2 d.p.)
The zero shows we have rounded to two decimal places
(iii) Identify the second decimal place (9)
Circle the digit to the right of the second decimal place (8)
As this digit is greater than or equal to 5 we will round the number up
5.00 (2 d.p.)
Two zeros show we have rounded to 2 decimal places
How do I round a number to a given significant figure?
To find the first significant figure when reading from left to right, find the biggest place value that has a non-zero digit
The first significant figure of 3097 is 3
The first significant figure of 0.0062070 is 6
The zeros before the 6 are not significant
The zero after the 2 but before the 7 is significant
The zero after the 7 is not significant
Count along to the right from the first significant figure to identify the position of the required significant figure
Do count zeros that are between other non-zero digits
E.g. 0 is the second significant figure of 3097
9 is the third significant figure of 3097
Use the normal rules for rounding
For large numbers, complete places up to the decimal point with zeros
E.g. 34 568 to 2 significant figures is 35 000
For decimals, complete places between the decimal point and the first significant figure with zeros
E.g. 0.003 435 to 3 significant figures is 0.003 44
How do I know what degree of accuracy to give my answer to?
If a question requires your answer to be an exact value
You can leave it as a simplified fraction
E.g.
You can leave it in terms of or a square root
E.g. , or
If it is an exact decimal up to and including 5 s.f., you can write it out without rounding it
E.g. 0.9375, or 850.25
If the answer is not exact, an exam question will often state the required degree of accuracy for an answer
E.g. Give your answer to 2 significant figures
If the degree of accuracy is not asked for, use 3 significant figures
All working and the final answer should show values correct to at least 4 significant figures
The final answer should then be rounded to 3 significant figures
In money calculations, unless the required degree of accuracy is stated in the question, you can look at the context
Round to 2 decimal places
E.g. $64.749214 will round to $64.75
Or to the nearest whole number, if this seems sensible (for example, other values are whole numbers)
$246 029.8567 rounds to $246 030
When calculating angles, all values should be given correctly to 1 decimal place
An angle of 43.5789 will round to 43.6
An angle of 135.211... will round to 135.2°
Examiner Tips and Tricks
In an exam question check that you have written your answer correctly by considering if the value you have ended up with makes sense
Remember the importance of zeros to indicate place value
E.g. Round 2 530 457 to 3 significant figures, 253 (without the zeros) and 2 530 000 are very different sizes!
Worked Example
Round the following numbers to 3 significant figures.
(i) 345 256
(ii) 0.002 956 314
(iii) 3.997
(i) The first (non-zero) significant digit is in the hundred thousands column (3)
The third significant figure is therefore the value in the thousands column (5)
Circle the digit on the right of the third significant figure (2)
This digit is less than 5 so round down
345 000 (3 s.f.)
(ii) The first significant digit is in the thousandths column (2)
The third significant figure is therefore in the hundred thousandths column (5)
Circle the digit to the right of the third significant figure (6)
6 is greater than 5 so we need to round up
0.002 96 (3 s.f.)
(iii) The first significant digit is in the units column (3)
The third significant figure is therefore in the hundredths column (9)
Circle the digit to the right of the third significant figure (7)
This value is greater than 5 so it will round up
4.00 (3 s.f.)
The two zeros indicate that it has been rounded to 3 s.f.
Why do I need to estimate?
Estimation can be used to find approximations for difficult calculations
You can estimate a calculation to check your answers
You can identify if there is a mistake in your working out if your answer is much bigger or smaller than your estimated value
How do I estimate?
Round each number in the question to a sensible degree, then perform the calculation
The exam question will usually tell you what to round each number to before carrying out any calculations
The general rule is to round numbers to 1 significant figure
7.8 ➝ 8
18 ➝ 20
3.65 × 10-4 ➝ 4 × 10-4
1080 ➝ 1000
In certain cases it may be more sensible (or easier) to round to something convenient
16.2 ➝ 15
9.1 ➝ 10
1180 ➝ 1200
Avoid rounding values to zero
How do I know if I have underestimated or overestimated?
For addition a + b and multiplication a x b
a (rounded up) and/or b (rounded up) | Overestimate | |
a (rounded down) and/or b (rounded down) | Underestimate |
For subtraction a - b and division a ÷ b
a (rounded up) and/or b (rounded down) | Overestimate | |
a (rounded down) and/or b (rounded up) | Underestimate | |
a (rounded up) and b (rounded up) | Not easy to tell | |
a (rounded down) and b (rounded down) | Not easy to tell |
Examiner Tips and Tricks
Estimation exam questions often involve small decimals
Avoid rounding to 0, especially if the small decimal is the denominator of a fraction, as dividing by 0 is undefined
Worked Example
Calculate an estimate for .
State, with a reason, whether the estimate is an overestimate or an underestimate.
Round each number to 1 significant figure
17.3 → 20
3.81 → 4
11.5 → 10
Perform the calculation with the rounded numbers
An estimate is 8
This is an overestimate as the numerator was rounded up and the denominator was rounded down
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