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Succeed with maths: part 1
Succeed with maths: part 1

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1 Fractions and decimals

You use fractions every day even if you're not really thinking about it. For example, if somebody asks you the time it could be half left parenthesis one divided by two right parenthesis past 2 or a quarter left parenthesis one divided by four right parenthesis to 6. The half and the quarter are parts of an hour; in other words they are fractions of a whole.

The number at the bottom of the fraction tells you how many parts the whole one has. So, one divided by two has two parts in the whole one and one divided by four has 4. The number at the top tells you how many of these parts there are. Hence, one divided by two is 1 lot of 2 parts. You’ll be looking at this again in more detail in Week 3.

Since fractions are parts of a whole, just as decimals are, this means that you can relate fractions and decimals. Here you will only be dealing with fractions that are easily shown in a place value table.

So, say you needed to write out 2 and three divided by 10 (three-tenths) as a decimal. The whole part is 2 and the fractional part is three divided by 10. Remember in order to separate the whole number from the fraction you use a decimal point, with the part of the whole number to the right. So, you would write the 2 to the left of the decimal point and the fractional part to the right of the decimal point. Thus, it would be written as 2.3. If you were dealing with three divided by 10 on its own, you would need to show that there were no whole parts by showing a zero to the left of the decimal point. three divided by 10 is therefore written as 0.3.

Now you’ve seen a few examples, it’s your turn to have a try yourself in the next activity. You can use a place value table if it helps you.

Activity 1 Fractions to decimals

Timing: Allow approximately 10 minutes

a) Rewrite each of the following fractions as a decimal number.

  • i.two divided by 10

    Remember: if the number does not have a whole number part, a zero is written in the units place. This makes the number easier to read (it’s easy to overlook the decimal point).


  • i.two divided by 10 equals 0.2
  • ii.three divided by 10


  • ii.three divided by 10 equals 0.3
  • and two divided by 10


  • and two divided by 10 equals 1.2
  • iv.three postfix times and three divided by 100


  • iv.three postfix times and three divided by 100 equals 3.03

b) Match the numbers below to the letter shown on the number line in Figure 1.

A number line from 0 to 4 marked out in intervals of 0.1. A to D point at different places along the line.
Figure 1 Number line exercise

Using the following two lists, match each numbered item with the correct letter.

  1. B

  2. C

  3. A

  4. D

  • a.0.3

  • b.3.0

  • c.three and two divided by 10

  • and three divided by 10

The correct answers are:
  • 1 = b
  • 2 = a
  • 3 = d
  • 4 = c

Now, you’re going to turn your attention to rounding numbers, and making estimates. Understanding place value will help with this, but you’ll also investigate the idea of decimal places when rounding.