Rounding & Estimation (Edexcel IGCSE Maths A (Modular))

Revision Note

Flashcards

Did this video help you?

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)

345.25 circle enclose 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)

0.29 circle enclose 5 space 631 

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)

4.99 circle enclose 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. 5 over 6

    • You can leave it in terms of pi or a square root

      • E.g. 4 pi, or square root of 3

    • 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 43.5789degree will round to 43.6degree

    • An angle of 135.211...degree 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)

345 space circle enclose 2 56

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)

0.002 space 95 circle enclose 6 space 314

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)

3.99 circle enclose 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 fraction numerator 17.3 cross times 3.81 over denominator 11.5 end fraction.
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

fraction numerator 20 cross times 4 over denominator 10 end fraction equals 80 over 10 equals 8

An estimate is 8

This is an overestimate as the numerator was rounded up and the denominator was rounded down

Last updated:

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.