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4.5 Fractions and Decimals

GCSE Maths Foundation · Edexcel · Chapter 4: Fractions and percentages

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: converting between fractions and decimals, recurring decimals and ordering. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Write a terminating decimal as a fraction in its simplest form
  • Write a fraction as a decimal, using equivalent fractions or division
  • Recognise recurring decimals and write them with dot notation
  • Order a mixture of fractions and decimals

Key words

  • Terminating decimal: A decimal that stops, e.g. 0.375.
  • Recurring decimal: A decimal with a digit or block of digits that repeats for ever, e.g. 0.333…
  • Dot notation: Dots over the first and last repeating digits show which digits recur.
  • Place value: The value of a digit from its position: tenths, hundredths, thousandths …

Decimals to fractions

Use place value. The last digit tells you the denominator: tenths → /10, hundredths → /100, thousandths → /1000. Then simplify.

Worked example: decimal to fraction

0.6 = 6/10 = 3/5
0.35 = 35/100 = 7/20
2.45 = 2 45/100 = 2 9/20

Answer: 3/5, 7/20, 2 9/20

Fractions to decimals

If the denominator is a factor of 10, 100 or 1000, write an equivalent fraction with that denominator. Otherwise divide the numerator by the denominator using short division.

Worked example: equivalent fraction

3/25 = 12/100 = 0.12 (× 4 top and bottom)
7/20 = 35/100 = 0.35 (× 5 top and bottom)

Answer: 0.12 and 0.35

Worked example: short division

3/8 = 3 ÷ 8. Write 3 as 3.000 and divide:
8 into 30 = 3 r 6; 8 into 60 = 7 r 4; 8 into 40 = 5 r 0.

Answer: 3/8 = 0.375

  • Decimal; 1/2 0.5; 1/4 0.25; 3/4 0.75; 1/5 0.2; 1/8 0.125; 1/10 0.1; 1/3 0.333…; 2/3 0.666…

Key fact: Learn the common ones in the table: they make many questions quick.

Recurring decimals

Some fractions give decimals that never end. When you divide, a remainder repeats, so the digits repeat. We put a dot over a repeating digit, or over the first and last digits of a repeating block.

Worked example: finding a recurring decimal

5/6 = 5 ÷ 6: 6 into 50 = 8 r 2; 6 into 20 = 3 r 2; 6 into 20 = 3 r 2 … the 3 repeats.
So 5/6 = 0.8333…, written 0.83 with a dot over the 3.

Answer: 0.8333… (the 3 recurs)

A fraction in its simplest form gives a terminating decimal only if its denominator has no prime factors other than 2 and 5. For example 7/40 terminates (40 = 2 × 2 × 2 × 5) but 5/12 recurs (12 has a factor 3).

Ordering fractions and decimals

Change everything to decimals (or to percentages), line up the decimal points, then compare.

Worked example: ordering

Order 5/8, 0.7, 2/3, 0.55, 3/5 from smallest to largest.
5/8 = 0.625, 2/3 = 0.666…, 3/5 = 0.6
0.55 < 0.6 < 0.625 < 0.666… < 0.7

Answer: 0.55, 3/5, 5/8, 2/3, 0.7

Common mistakes

  • Writing 0.35 as 35/10, or 1/8 as 0.8.
  • Using the wrong denominator: 0.08 is 8/100, not 8/10.
  • Thinking 0.3 and 1/3 are equal: 1/3 = 0.333…, which is a little bigger than 0.3.
  • Comparing 0.7 and 0.65 by length: 0.70 is bigger than 0.65.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 3/8 as a decimal.

Answer: 0.375

Working: 3 ÷ 8 = 0.375.

Question 2. Write 0.65 as a fraction in its simplest form. (Type your answer like 2/5.)

Answer: 13/20

Working: 65/100 = 13/20.

Question 3. Write 7/25 as a decimal.

Answer: 0.28

Working: 7/25 = 28/100 = 0.28.

Related lessons

Continue in the full course

This lesson is section 4.5 (EGCMF0405) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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