Fractions to Decimals

A fraction and a decimal are two ways of writing one number. Children who see that clearly get percentages almost for free later, and children who do not spend years converting things they could have recognised.

Fractions · topic 9 of 9Grades 5 to 7Number8 min read7 practice questions

The same number twice

A hundred square settles this quickly. The grid holds exactly 100 small squares, so shading part of it is literally counting hundredths.

50 of the 100 squares shaded
Half the grid is shaded. That is 50100, which is 0.5, which is 50 percent. One picture, three names.

Shade a quarter of the grid instead and you get 25 squares.

25 of the 100 squares shaded
A quarter is 25 hundredths. As a decimal that is 0.25, and as a percentage it is 25 percent.

Nothing is really being converted here. The shaded area never changes size, whatever you decide to call it, and the word conversion makes the process sound more mysterious than it is.

Method 1, make it tenths or hundredths

Decimals are built out of tenths, hundredths and thousandths, so a fraction that already sits over 10, 100 or 1000 can simply be read off as a decimal with no working at all.

The rule

Use the equivalent fraction rule to get a denominator of 10, 100 or 1000. Then the numerator is your decimal digits.

34: multiply top and bottom by 25 to get 75100, which is 0.75.

75 of the 100 squares shaded
Three quarters of the grid is 75 squares. Seventy five hundredths, written 0.75.

This route is fast and it keeps the meaning in view, which matters at this age. It only works when the denominator goes into 10, 100 or 1000, and that covers 2, 4, 5, 8, 10, 20, 25 and 50, which is most of what a child will meet.

Method 2, just divide

The fraction line has always meant divide. 34 means 3 divided by 4.

So work out 3 ÷ 4 as a short division, adding a decimal point and as many zeros as the division needs, and 0.75 falls out.

Division always works, including for denominators like 3, 6 and 7, where no amount of multiplying will ever produce 10, 100 or 1000.

Which number goes inside the division?

The top one. 34 is 3 ÷ 4, not 4 ÷ 3. A quick sanity check: 34 is less than 1, so the decimal must start with 0. If you get 1.33 you divided the wrong way round.

Some fractions never finish. 13 gives 0.333 and the threes carry on forever. That is called a recurring decimal, and it is usually rounded or written with a dot above the repeating digit.

Worth learning by heart

These eight come up constantly, in tests and in life. Knowing them saves working out the same thing hundreds of times.

  • 12 = 0.5 = 50 percent
  • 14 = 0.25 = 25 percent
  • 34 = 0.75 = 75 percent
  • 15 = 0.2 = 20 percent
  • 25 = 0.4 = 40 percent
  • 110 = 0.1 = 10 percent
  • 18 = 0.125 = 12.5 percent
  • 13 = 0.333 and so on, about 33.3 percent

Worked examples

1

Using equivalent fractions

Write 25 as a decimal.
  1. Can 5 be turned into 10, 100 or 1000? Yes, 5 × 2 = 10.
  2. Do the same to the top. 2 × 2 = 4, giving 410.
  3. Four tenths is written 0.4.
  4. Check: 2/5 is a bit less than a half, and 0.4 is a bit less than 0.5.
25 = 0.4
2

Using division

Write 58 as a decimal.
  1. 8 does divide into 1000, but the easier route here is division.
  2. Work out 5 ÷ 8. Since 8 does not go into 5, start with 0 point.
  3. 8 into 50 goes 6 times with 2 left. 8 into 20 goes 2 times with 4 left. 8 into 40 goes 5 times exactly.
  4. Reading the digits off gives 0.625.
58 = 0.625
3

Simplify first, then convert

Write 1560 as a decimal.
  1. Those numbers look awkward, so simplify before doing anything else.
  2. Both divide by 15. 15 ÷ 15 = 1 and 60 ÷ 15 = 4, giving 14.
  3. A quarter is one of the eight worth knowing by heart.
  4. Simplifying first turned a long division into something you already knew.
1560 = 0.25

Common mistakes

1. Dividing the wrong way round

34 gets worked out as 4 ÷ 3, giving 1.33, usually because dividing the smaller number by the bigger one feels wrong. The top number always goes inside the division, and there is a free check attached: a fraction under 1 must give a decimal starting with 0, so anything beginning with a 1 is a signal to start again.

2. Reading the digits straight off the fraction

14 is written as 0.14 and 12 as 0.12, which is a reasonable guess if nobody has ever said otherwise. The digits in a fraction have no direct relationship to the digits in its decimal, and only a denominator of 10, 100 or 1000 lets anything be read off without working.

3. Losing a place value

3100 becomes 0.3 rather than 0.03, and the missing zero makes the answer ten times too big. Saying the fraction out loud first fixes almost all of these, because a child who has just said "three hundredths" will not write a 3 in the tenths column.

Practice questions

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For parents

Of everything in this topic, the eight conversions listed above repay memorising more than anything else. Five minutes of flashcards two or three times a week is enough, and after a fortnight your child will stop calculating that three quarters is 0.75 and simply know it. That sounds like a small saving until you watch a percentage question, where the child who recognises the numbers has their whole attention free for the part that actually carries the marks.

Keep going

Maths CheckTwelve questions, five minutes, then a printable report naming what to work on next. Free, no sign up.OpenShow me the workingLong division, long multiplication and column methods, walked step by step on your own numbers.Open

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