# 2.3 Recognise and represent decimal fractions

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## Recognise and represent fractions

Activity 1:

To recognise and represent decimal fractions [LO 1.3]

RECOGNIZING DECIMALS

1. What are decimals?

1.2 Think back to Place Value: Thousands; Hundreds; Tens and Units.

Complete the following:

 1 000  10 = 100 100  10 = 10  10 = 110 = ?

The calculator says that 1 10 = 0,1. What does 0,1 then mean? Discuss with a friend.

1.4 Draw lines on the bar below to show tenths. One has been divided by 10. We say that 0,1 is one tenth. It is the only way in which calculators can write one tenth, because of the way that they have been programmed. Now label each section on the bar below 0,1.

What is the meaning of 0,1? We have found that 1  10 = 0,1.

Think back to Fractions: we said: 1  2 = $\frac{1}{2}$

So 1  10 = $\frac{1}{\text{10}}$

1  10 = $\frac{1}{\text{10}}$ = 0,1

0,1 is just another way of writing $\frac{1}{\text{10}}$

Study the diagram:

 Thousands1 000 Hundreds100 Tens10 Units1 Tenths
 Thousands1 000 Hundreds100 Tens10 Units1 Tenths $\frac{1}{\text{10}}$ 7 1 9 3 6 5 0 6 9 1

How do we show the end of the whole number when there are no headings?

We use a DECIMAL COMMA.

What are the numbers that have been written in the columns?

• 7 193, 6 = 7 × 1 000 + 1 × 100 + 9 × 10 + 3 × 1 + six tenths
• 5 069,1 = 5 × 1 000 + 0 + 6 × 10 + 9 × 1 + $\frac{1}{\text{10}}$

Our calculators cannot write common fractions as we can; they are only machines that have been programmed to use place value, so they can only write decimal fractions.

Remember: We use a DECIMAL COMMA

to show the END OF THE WHOLE NUMBER

and the BEGINNING OF THE DECIMAL FRACTION

2. Now write the following decimal numbers in their expanded form under the correct heading in the columns below:

2.1 (a) 1 456,3 (b) 4 601,9 (c) 8,5 (d) 31, 7 (e) 456,2

 X 1 000 × 100 × 10 × 1 × 0,1(tenths) (a) (b) (c) (d) (e)

The FIRST digit after the decimal comma is always TENTHS.

2.2 Now write them again in their expanded form:

(a) 1 456,3 = 1 × 1 000 + 4 × 100 + 5 × 10 + 6 × 1 + 3 × 0,1

Activity 2:

To compare fractions [LO 1.5]

1. Carefully consider the value of each digit and use the correct sign from:<;  ; = to>compare the following:

1.1 1,5 _____1,7 1.4 45,9 ____62,3

1.2 6,3 ____ 6,1 1.5 13,2 ____8,6

1.3 24,7____ 42,3 1.6 57,5 ____58,2

2. Encircle the largest number:

43,7; 41,9; 43,1; 49,1; 41,5

3. Write down the number that is:

 Answer Answer 3.1 one more than 9,9 3.1 3.5 0,1 less than 7,1 3.5 3.2 0,1 more than 5,3 3.2 3.6 0,1 more than 99,0 3.6 3.3 0,1 less than 6 3.3 3.7 0,1 more than 5,8 3.7 3.4 0,1 less than 8,3 3.4 3.8 0,1 less than 10 3.8

Activity 3:

To convert from fractions to decimal fractions and vice versa [LO 1.5]

Group discussion.

1. Read the following conversation between John and Sarah.

• Was Sarah’s answer correct? It did not seem to help John completely. Where did the ,5 come from? Discuss. Try to explain why half = 0,5 on a calculator.
• Which of you were wide awake? All of you? Did you all know? Wonderful! Yes, it’s because the calculator counts in tenths and five-tenths = one-half. The poor calculator has to use equivalent fractions to make tenths from things like halves and quarters and any fractions that are not tenths (hundredths and thousandths, but they come later).

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