# Unit 17 Section 1 : Converting Decimals into Fractions

In this unit we revise some aspects of decimals and then learn about converting decimals to fractions.

Place Value
Each of the digits in a number has a different value, because of the place values.

Converting Decimals to Fractions
Now think about the number 0.27:

One tenth is the same as ten hundredths, so two tenths must be the same as twenty hundredths.
This means that 0.27 can also be thought of as 27 hundredths or.

 In the same way, 0.127 is 127 thousandths or. The fractions you need to know in order to convert decimals to fractions are shown on the right: Examples
You can see that some fractions may be simplified (or cancelled down) after conversion.
Also, if you convert a number which is larger than 1, you will get a vulgar or improper (top-heavy) fraction.

Sorting decimals into order
If we want to sort some decimal numbers into order, it is easier to compare them if you use the same number of decimal places for each number.

For example, imagine we want to sort the numbers 0.7, 0.17, 0.77, 0.71, 0.701 and 0.107 into ascending order.
Writing each to 3 decimal places gives: 0.700, 0.170, 0.770, 0.710, 0.701 and 0.107.
It's now easier to see the order should be: 0.107, 0.170, 0.700, 0.701, 0.710, 0.770.

So the answer is: 0.107, 0.17, 0.7, 0.701, 0.71, 0.77.

## Example Questions

Work out the answer to each of these questions then click on the button marked to see whether you are correct.

(a) Convert 0.51 to a fraction.

(b) Convert 0.125 to a fraction.

(c) Sort into ascending order: 0.37, 0.733, 0.037, 0.7, 0.07, 0.307.

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.
 Some questions have fractions as answers.Put the numerator in the top box and the denominator in the bottom box, for example:

Question 1
What is the value of the 7 in each of the numbers below:

(a) 0.714

(b) 0.070

(c) 7.042

(d) 0.007

(e) 0.471

(f) 0.157

Question 2
Write each list of numbers in order with the smallest first:

(a) 0.61, 0.16, 0.601, 0.106, 0.661, 0.616

(b) 0.47, 0.82, 0.4, 0.78, 0.28

(c) 0.32, 0.23, 0.2, 0.301, 0.3

(d) 0.17, 0.19, 0.9, 0.91, 0.79

Question 3
Write each of these decimals as a fraction, giving them in their simplest form:

 (a) 0.1 =
 (b) 0.9 =
 (c) 0.07 =
 (d) 0.25 =
 (e) 0.05 =
 (f) 0.003 =
 (g) 0.71 =
 (h) 0.65 =

Question 4
Write each of these decimals as a fraction and simplify where possible:

 (a) 0.4 =
 (b) 0.08 =
 (c) 0.006 =
 (d) 0.012 =
 (e) 0.84 =
 (f) 0.008 =
 (g) 0.375 =
 (h) 0.48 =

Question 5
Fill in the missing numbers below:
 (a) 0.6 = 5
 (b) 0.14 = 50
 (c) 0.18 = 50
 (d) 0.008 = 125
 (e) 0.012 = 250
 (f) 0.032 = 125

Question 6
Write these numbers as improper fractions in their simplest form:

 (a) 1.2 =
 (b) 3.02 =
 (c) 4.12 =
 (d) 3.62 =
 (e) 4.008 =
 (f) 5.015 =

Question 7
Calculate the answers to these questions, and give your answers (i) as decimals, and (ii) as fractions.
(a) 0.7 + 0.6 (i)
 (ii)
(b) 8.21 - 0.31 (i)
 (ii)
(c) 0.06 + 0.3 (i)
 (ii)
(d) 3.04 - 0.2 (i)
 (ii)

Question 8
Work out the missing decimals in these questions, then convert them to fractions in their simplest form:

 (a) 0.20 + ? = 0.81 (b) 0.42 + ? = 0.53 (c) 0.91 - ? = 0.47 (d) 0.92 - ? = 0.58

Question 9
Convert these decimals to fractions in their simplest form.
You might need pen and paper because some answers need a lot of simplifying.

 (a) 0.0001 (b) 0.0009 (c) 0.1475 (d) 0.00008 (e) 0.00102 (f) 0.02222

You have now completed Unit 17 Section 1
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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