Fraction to decimal

Primary 5 Fraction and Division study guide: the whole chapter, step by step

About this subtopic

Divide the top number by the bottom number to write a fraction as an exact or corrected decimal.

Lesson video, with the working

Fraction to decimal

3 min 11 s

The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.

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Today's question

Express 7/20 as a decimal.

  1. 7/20 = 35/100 = 0.35

Ans: 0.35

Example 1

Express 5/7 as a decimal. Correct your answer to 2 decimal places.

  1. 5 ÷ 7 ≈ 0.71 correct to 2 decimal places

Ans: 0.71

How to solve it
  1. A fraction line means divided by. Seven over twenty means 7 divided by 20.
  2. Try a denominator of 10 or 100. 20 goes into 100 five times, so multiply the top and the bottom by 5.
  3. 7 times 5 is 35, so seven over twenty is 35 over 100, which is 0.35.
  4. If neither works, divide the top by the bottom, as in 5 divided by 7. Work to one more decimal place than asked.
  5. 5 divided by 7 begins 0.714. The third decimal digit is 4, less than 5, so the second digit stays the same: 0.71.

To correct to two decimal places, look at the digit in the third decimal place.

Practice questions with worked solutions

Question 1 is free to try. The other 10 open in the free trial, each with its full working.

Challenge

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10 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 13 · Basic · free to tryExpress 7/9 as a decimal. Correct your answer to 2 decimal places.Express 7/9 as a decimal…

Express 7/9 as a decimal. Correct your answer to 2 decimal places.

Show the working and the answer

Video solution · 1 min 19 s

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Working

101007.00090.777637063706370.78
  1. decimal form = 7/9 = 7 ÷ 9
  2. 7 ÷ 9 = 0.777…
  3. the third decimal place is 7, which is 5 or more, so the second decimal place goes up from 7 to 8
  4. 7 ÷ 9 = 0.78 (to 2 decimal places)

Answer: 0.78

For parents

How do you solve P5 fraction to decimal questions?

This page covers the Primary 5 outcome on expressing fractions as decimals, for proper fractions, improper fractions and mixed numbers, with and without rounding.

What your child learns here

This page covers the Primary 5 outcome on expressing fractions as decimals, for proper fractions, improper fractions and mixed numbers, with and without rounding.

  • If the denominator divides 10, 100 or 1000 exactly, write an equivalent fraction with that denominator and read off the decimal.
  • Otherwise divide the numerator by the denominator by long division.
  • For a mixed number, keep the whole number and convert only the fraction part.
  • When a number of decimal places is asked, work to one more place, then round.
  • If no rounding is asked, keep dividing until there is no remainder.
Does the answer make sense?

A proper fraction must become a decimal less than 1, an improper fraction one greater than 1, and for a mixed number your child keeps the whole number in front of the decimal point. So 17/6 must come out between 2 and 3, and 3/40 well under one tenth.

How to practise these questions

Basic questions train rewriting fractions over 10 or 100, using long division when that is not possible, and rounding to 1 or 2 decimal places. The Challenge questions round where the deciding digit is exactly 5, keep the whole number apart from a recurring fraction part, or set the division inside a story. If the rounding or the long division slips, watch the solution film for that question and try it again later from Revision. Its multiple-choice Basic questions give a division and ask which of four forms, decimals among them, is NOT equal to it, with each option checked in the written working instead of a film.

Questions parents ask

Is changing fractions to decimals in Primary 5? Yes. Expressing fractions as decimals is an outcome under Fraction and Division in the Primary 5 syllabus.

When should my child use long division? When the denominator cannot be made into 10, 100 or 1000, such as 3 or 7, divide the numerator by the denominator. Fractions such as fifths, quarters and eighths can be rewritten instead.

How do I round to 2 decimal places? Work out three decimal places, then look at the third digit. If it is 5 or more, round the second digit up; otherwise leave it as it is.