Skip to content
Cambridge IGCSE0607

Estimation

International Mathematics 0607 Chapter Notes

What this chapter covers

Estimation
ShareWhatsAppPost
Estimation notes

Read online free. Download a watermarked copy with a free account.

Read the notes

The full Estimation notes as text: skim, search, and jump between subtopics.

~5 min read

In this chapter

  1. 1Rounding to the nearest 10, 100 or 1 000
  2. 2Decimal places and significant figures
  3. 3Estimating a calculation
  4. 4Round the final answer only
  5. 5Rounding to suit the problem

1. Rounding to the nearest 10, 100 or 1 000

To round a value, find the place the question names. Then look at the digit one place to its right. If that digit is 5 or more, round up. If it is less than 5, leave the digit alone.

Place-value rounding is to the nearest 10, the nearest hundred or the nearest thousand. Every digit after the rounded place becomes a zero. For example, 5764 correct to the nearest thousand is 6000.

Examiner insight

“Most of the candidates could find the correct answer but not all of them managed to round their answer to the nearest hundred.”

Worked example 11 mark

Write 45 193 correct to the nearest hundred.

  1. 1

    The hundreds digit is 1. The next digit is 9, so round up: 45 200 [1]

2. Decimal places and significant figures

Decimal places count digits after the decimal point. Significant figures count from the first non-zero digit. Zeros before that digit are never significant.

A zero at the end of a rounded decimal stays, because it shows the accuracy: 705.180 is 3 decimal places. Do not move the digits around the decimal point.

Examiner insight

“Candidates were better at rounding to the nearest 10 than dealing with decimal places or significant figures.” “Sometimes the answer to part (a) only had 1 significant figure or the number was moved around the decimal point but kept the same digits.”

Worked example 11 mark

Write 705.180 20 correct to 3 decimal places.

  1. 1

    The third decimal place is 0. The next digit is 2, so round down: 705.180 [1]

3. Estimating a calculation

To make an estimate, write each number in the calculation correct to 1 significant figure. Then work the calculation with the rounded numbers. This should be possible without a calculator.

Round every number, including the ones inside brackets. A decimal such as 0.5461 rounds to 0.5, not to 1.

Examiner insight

“Some did not round any of the numbers and proceeded to work out the actual answer by long multiplication, subtraction and division.” “The major error seen was to round 0.5461 to 1.”

Worked example 12 marks

By writing each number correct to 1 significant figure, find an estimate of

(5.1 × 19.5)/(6.9 - 3.3).

  1. 1

    Round each number: (5 × 20)/(7 - 3) [1]

  2. 2

    = 100/4 = 25 [1]

4. Round the final answer only

An estimate rounds the numbers first. An accurate answer does the opposite. Work out the whole calculation, then round the final answer to the accuracy the question asks for.

On a calculator, enter the whole expression with brackets round the bottom line. Read the full display, then round it. Never copy a rounded middle value back in.

Examiner insight

“Sometimes the answer was spoiled by rounding the radius prematurely to 1.65 so that the final answer was about 1 cm out.” “Some candidates rounded an intermediate value leading to a final answer outside the acceptable range.”

Worked example 12 marks

Work out (3.82 × 5.23)/(1.63 - 1.17).

Give your answer correct to the nearest 10.

  1. 1

    Enter 3.82 × 5.23 ÷ (1.63 - 1.17) and read the display: 43.4… [1]

  2. 2

    Round the final answer to the nearest 10: 40 [1]

5. Rounding to suit the problem

The context decides how to round. A count of whole objects must be a whole number. If you need enough to cover everyone, round up. If you can only buy what you can afford, round down.

Read the question again after the calculation. Ask what the number measures, and give an answer that makes sense in the context.

Examiner insight

“Some candidates lost accuracy through rounding 37.94… to 37 which was incorrect in the context of the question.” “Some candidates rounded their answer up rather than down.”

Worked example 12 marks

A coach holds 52 passengers. 340 pupils go on a trip. How many coaches are needed?

  1. 1

    340 ÷ 52 = 6.538… [1]

  2. 2

    A part-filled coach is still a coach, so round up: 7 coaches [1]

Recap

  • Rounding: look at the digit one place to the right. 5 or more rounds up.
  • Decimal places count after the point. Significant figures count from the first non-zero digit.
  • Estimate: round each number to 1 significant figure, then calculate.
  • Accurate answer: calculate everything first and round only the final answer.
  • In context: round up to have enough, round down to stay within what you have.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. Write 6748 correct to the nearest hundred.1 mark
  2. Do not use a calculator. Write 0.04852 correct to 2 significant figures.1 mark
  3. Write 12.0961 correct to (a) 2 decimal places (b) 3 significant figures.2 marks
  4. Do not use a calculator. Write 3 967 000 correct to 2 significant figures.2 marks
  5. Do not use a calculator. By writing each number correct to 1 significant figure, estimate the value of 41.3/(9.79 × 0.765).3 marks
  6. Use a calculator to work out (7.84 × 6.15)/(3.28 - 1.91). Give your answer correct to the nearest 10.3 marks
  7. Do not use a calculator. By writing each number correct to 1 significant figure, estimate (3.9 × 81.2)/0.0405.3 marks
  8. Each gift needs 0.35 m of ribbon. A roll of ribbon is 5.5 m long. How many whole gifts can be wrapped from one roll?2 marks
  9. A wall is a rectangle 8.65 m long and 2.74 m high. It needs two coats of paint. One tin of paint covers 13.5 m². Sami rounds the area of the wall to the nearest 10 m² and then works out how many tins to buy. (a) Work out the number of tins Sami buys. (b) Work out the number of tins that are needed.4 marks
  10. A hall floor is a rectangle 18.6 m by 11.4 m. Each chair needs 0.48 m² of floor. Chairs are hired in stacks of 25. Each stack costs 31.75 dollars. (a) By writing each number correct to 1 significant figure, estimate the number of chairs that fit in the hall. (b) Calculate the greatest number of chairs that fit in the hall. (c) A school has 550 dollars to spend. Show that the school cannot hire enough chairs to fill the hall.7 marks

Free notes are just the start.

Unlock every Workbook and Chapter at a Glance, and generate your own worksheets and predicted papers.

Explore plans

Related chapters

Types of numberSetsPowers and rootsFractions, decimals and percentagesOrderingThe four operations