Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Checking and securing understanding of converting between fractions and decimals

      Lesson details

      Learning outcome

      I can convert fractions to decimals and decimals to fractions.

      Key learning points

      1. The line in a fraction is referred to as the fraction bar or vinculum and in a fraction this represents division.
      2. Dividing the numerator by the denominator may result in an equivalent terminating decimal.
      3. If the decimal is non-terminating then the decimal is an approximation of the fraction.
      4. Writing the decimal as a fraction with a denominator of one allows you to use your knowledge of equivalent fractions.
      5. Through equivalent fractions, you can write a fraction where the numerator is an integer value.

      Keywords

      • Vinculum - Vinculum is the horizontal line placed over an expression to show that everything below that line is one group.

      Common misconception

      When ordering decimals, the more significant figures the greater the number.

      When ordering decimals, having the same number of decimal places allows the pupils to see the magnitude of the number more clearly.

      Teacher tip

      Creating their own questions using common equivalents helps embed the required knowledge of these common equivalents. E.g Create questions where numbers need to be ordered. E.g Create questions where the sum of two common equivalents is greater than the third. Checking with a calculator helps.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      A ___________ decimal is one that has a finite number of digits after the decimal point.

      fast
      Correct answer: terminating
      solid
      finished
      recurring

      Q2.
      Which of the following is a mixed number?

      $${{4} \over {3}}$$
      Correct answer: $$6 {{2} \over {3}}$$
      $$ {{5} \over {8}}$$
      $$ {{4} \over {9}}$$

      Q3.
      Which of the following is equivalent to $$ {{2} \over {3}}$$?

      Correct answer: $$ {{4} \over {6}}$$
      Correct answer: $$ {{8} \over {12}}$$
      $$ {{4} \over {5}}$$
      Correct answer: $$ {{6} \over {9}}$$

      Q4.
      Which of the following is equivalent to $$\frac{4}{10}$$?

      $$\frac{8}{10}$$
      Correct answer: $$\frac{2}{5}$$
      $$\frac{1}{4}$$

      Q5.
      Which of the following is equivalent to $$\frac{5}{9}$$?

      Correct answer: $$\frac{15}{27}$$
      $$\frac{10}{9}$$
      $$\frac{20}{27}$$

      Q6.
      Which of the following is an improper fraction?

      $$\frac{9}{10}$$
      $$2 \frac{9}{10}$$
      Correct answer: $$\frac{10}{9}$$
      $$10.9$$

      6 Questions

      Q1.
      Which of these is equivalent to 0.312?

      $$\frac{312}{100}$$
      $$\frac{31}{120}$$
      Correct answer: $$\frac{39}{125}$$

      Q2.
      Which of these is equivalent to 0.42?

      Correct answer: $$\frac{21}{50}$$
      $$\frac{42}{1000}$$
      $$\frac{11}{25}$$

      Q3.
      Which of these is equivalent to 0.04?

      $$\frac{1}{5}$$
      Correct answer: $$\frac{1}{25}$$
      $$\frac{1}{50}$$

      Q4.
      Convert 13.6 into a mixed number.

      Correct answer: $$13 \frac{3}{5}$$
      $$13 \frac{68}{5}$$
      $$13 \frac{136}{10}$$

      Q5.
      Convert 9.4 into a mixed number.

      $$9 \frac{4}{5}$$
      Correct answer: $$9 \frac{2}{5}$$
      $$9 \frac{2}{10}$$

      Q6.
      Convert 12.3 into an improper fraction.

      $$\frac{1203}{10}$$
      $$\frac{1230}{10}$$
      Correct answer: $$\frac{123}{10}$$

      To help you plan your 10 maths lesson on: Checking and securing understanding of converting between fractions and decimals, download all teaching resources for free and adapt to suit your pupils' needs...