Rounding & Estimation (Cambridge (CIE) IGCSE Maths)

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)

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°

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

• For subtraction a - b and division a ÷ b