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KS2 Maths textbook

Chapter 7: Decimals and percentages

  • Strand Fractions and decimals
  • Level Year 5
  • Practice 101 questions with step-by-step solutions

National Curriculum for England, Key Stage 2 mathematics, Year 5. Content: Read and write decimal numbers as fractions; recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents, Round decimals with two decimal places to the nearest whole number and to one decimal place; read, write, order and compare numbers with up to three decimal places, Solve problems involving number up to three decimal places, Recognise the per cent symbol (%) and understand that per cent relates to number of parts per hundred; write percentages as a fraction with denominator 100 and as a decimal, Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with a denominator of a multiple of 10 or 25.

Open Year 5 chapter

By the end of this chapter you will be able to

  • Write decimals with tenths, hundredths and thousandths as fractions in their simplest form, and write fractions as decimals
  • Understand place value to three decimal places, and use zeros as place holders
  • Compare and order decimals with up to three decimal places
  • Round a decimal with two decimal places to the nearest whole number and to one decimal place
  • Add and subtract decimals with up to three decimal places by lining up the decimal points, and solve problems with them
  • Understand that per cent means out of 100, and change between percentages, fractions with denominator 100 and decimals
  • Know the percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25
  • Explain your reasoning about decimals and percentages, and spot the mistakes in other people’s working

You should already know

  • Tenths and hundredths as fractions, and equivalent fractions (Year 5 Chapter 6)
  • Dividing and multiplying whole numbers and decimals by 10, 100 and 1,000 (Chapters 4 and 5)
  • Place value of numbers up to 1,000,000 (Chapter 1)
  • Simplifying fractions and finding the highest common factor (Chapter 6)

Where this leads

  • Percentages of amounts, and comparing with percentages (Year 6)
  • Decimals with more places, and rounding to a given accuracy (Year 6)
  • Ratio and proportion, and conversion between fractions, decimals and percentages in Year 6

Lessons in this chapter

  1. 7.1 Tenths, hundredths and thousandths
  2. 7.2 Comparing and ordering decimals
  3. 7.3 Rounding decimals
  4. 7.4 Adding, subtracting and solving problems
  5. 7.5 Per cent
  6. 7.6 Fractions, decimals and percentages
  7. Summary and key words
  8. Check-up and SATs-style questions

Read the whole chapter on one page (good for printing).

Practise with real exam questions

The DfE publishes every past KS2 test, with mark schemes, for free.

KS2 Maths past papers