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      Converting fractions to terminating decimals

      Lesson details

      Learning outcome

      I can divide the numerator of a fraction by its denominator and know that this results in an equivalent terminating decimal.

      Key learning points

      1. The line in a fraction means divide.
      2. Dividing the numerator by the denominator may result in an equivalent terminating decimal.
      3. It can be shown that 1/2, 1/4 and 1/10 have equivalent terminating decimals.
      4. Using a calculator can help investigate fractions which are equivalent to terminating decimals.

      Keywords

      • Terminating decimals - A terminating decimal is one that has a finite number of digits after the decimal point.

      Common misconception

      Denominators that are multiples of 10 will give a terminating decimal.

      Investigate the difference between powers of 10 and multiples of 10. e.g 7/30 and 7/100

      Teacher tip

      After emphasising fractions must be in their simplest form and the denominator must have a product of its prime factors of 2 and/or 5, ask pupils to list as many non-terminating fractions in 1 minute where the denominator must be less than 100.

      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

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Fractions where the numerator is less than the denominator are called fractions.

      Correct Answer: proper

      Q2.
      The integer that is equivalent to the fraction $$30 \over 5$$ is .

      Correct Answer: 6, six

      Q3.
      Write $$3\frac{2}{7}$$ as an improper fraction.

      $$\frac{23}{2}$$
      $$\frac{21}{7}$$
      $$\frac{22}{7}$$
      Correct answer: $$\frac{23}{7}$$
      $$\frac{24}{7}$$

      Q4.
      Write the correct symbol (<, > or =) to make the statement true: $$17 \frac {1}{2} $$ $$\frac {69}{4} $$

      Correct Answer: >

      Q5.
      Starting with the smallest, put these fractions and mixed numbers in order of size.

      1 - $$1\frac {1}{8} $$
      2 - $$1\frac {1}{4} $$
      3 - $$\frac {13}{8} $$
      4 - $$1\frac {3}{4} $$
      5 - $$2\frac {1}{8} $$
      6 - $$\frac {18}{8} $$

      Q6.
      A gardener puts up a fence around a rectangular garden. Each fence panel is 1 metre long and costs £25. What is the total cost of the fencing? £

      An image in a quiz
      Correct Answer: 650, £650, 650.00, £650.00

      6 Questions

      Q1.
      Decimals that have a finite number of digits after the decimal point are called decimals.

      Correct Answer: terminating

      Q2.
      Without using a calculator, work out the decimal value of $$\frac {7}{8}$$.

      Correct Answer: 0.875, .875

      Q3.
      Select all the fractions that can be written as terminating decimals.

      Correct answer: $$\frac {7}{16}$$
      Correct answer: $$\frac {7}{5}$$
      $$\frac {7}{15}$$
      Correct answer: $$\frac {7}{20}$$
      $$\frac {7}{30}$$

      Q4.
      Sofia uses her calculator to convert $$0.3756$$ to a fraction. She gets an answer of $$\frac {939}{\square}$$. What number should go in the square?

      Correct Answer: 2500

      Q5.
      Match each fraction to its terminating decimal. You can use a calculator for this question.

      Correct Answer:$$\frac {82}{125}$$ ,$$0.656$$
      Correct Answer:$$\frac {3281}{5000}$$ ,$$0.6562$$
      Correct Answer:$$\frac {21}{32}$$,$$0.65625$$
      Correct Answer:$$\frac {26}{40}$$ ,$$0.65$$
      Correct Answer:$$\frac {180}{300}$$ ,$$0.6$$

      Q6.
      Lucas says that $$66 \over 1320$$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Lucas is correct or not.

      Lucas is correct as $$1320$$ has factors of $$3$$ and $$11$$
      Lucas is correct as only fractions with a denominator of $$10$$ terminate
      Correct answer: Lucas is wrong as the fraction simplifies to $$1\over20$$ which terminates
      Lucas is wrong as the denominator is a multiple of $$10$$
      Lucas is wrong as $$66$$ is a multiple of $$2$$

      To help you plan your 7 maths lesson on: Converting fractions to terminating decimals, download all teaching resources for free and adapt to suit your pupils' needs...