2.3 Recognise and represent decimal fractions  (Page 2/2)

With a calculator:

2. Make decimal fractions from the following:

2.1 $\frac{3}{4}$ = 3  4 = 0, ____

We can convert any ordinary fraction to decimals in that way.

3. Make one-third into a decimal: $\frac{1}{3}$ = 1  3 =_____

Can you think of a reason why the answer is the way it is?

Without a calculator:

4. Write down equivalent fractions for each of the following and then write them as decimal fractions:

(Some of the above have more than one decimal place but it is good to know about them.)

5. What about the thirds and sixths and others that cannot be made into tenths? Use division.

• one-third = 1  3 =
• two-thirds = 2  3 =

Use your own method for the division or use a calculator. $\frac{1}{3}$ = 1  3

Or one way: ? x 3 = 1

0 x 3 = 0,0

0,3 x3 = 0,9

0,03 x 3 = 0,09

0,99 (which is nearly 1)

so: (0 x 3) + ( 0,3 x 3) + ( 0,03 x 3)

0 + 0,3 + 0,03

= 0,333

(and the calculator will go on dividing: 0,333)

We say: 0,3 recurring or 0,3֯(The dot means recurring.)

TEST YOUR PROGRESS

1. Solve without a calculator:

1.1 17 × 26

1.2 153  9

2. Share 11 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

3. Share 12 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

4. Mike drinks $1\frac{1}{2}$ mugs of milk for breakfast. His sister, Sharon, drinks $\frac{3}{4}$ of a mug of milk. How much milk have they drunk altogether?

5. Write the following in expanded notation:

6. Write as decimals:

• Three and four-fifths = ………………………
• One and three-tenths = ………………….
• Five and one-quarter = …………………
• $4\frac{1}{2}$ = ………………….

7. From<;>; = write down the correct sign to make the following true:

• 2,4 ____ 4,2
• 1,7 _____2,1

8. Write down the number that is:

Assessement

Memorandum

ACTIVITY 1: recognising and representing decimal fractions

1.1 Missing numbers: 10; 1; one-tenth

1.2 Calculator answers: 10; 1; 0,1

0,1 means one-tenth

2.1

2.2 (b) 4 x 1 000 + 6 x 100 + 0 x 10 + 1 x 1 + 9 x 0,1

(c) 0 x 1 000 + 0 x 100 + 0 x 10 + 8 x 1 + 5 x 0,1 or just: 8 x 1 + 5 x 0,1

(d) 0 x 1 000 + 0 x 100 + 3 x 10 + 1 x 1 + 7 x 0,1 or just: 3 x 10 + 1 x 1 + 7 x 0,1

(e) 0 x 1 000 + 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1 or just: 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1

ACTIVITY 2: comparing decimal fractions

1.1<

1.2 

1.3<

1.4<

1.5 

1.6<

2. Encircled number: 49,1

3.1 10,9

3.2 5,4

3.3 5,9

3.4 8,2

3.5 7

3.6 99,1

3.7 5,9

3.8 9,9

ACTIVITY 3: converting from fractions to decimal fractions and vice versa

1. Discussion

2. With a calculator

• 0,75
• 2.2 0,4
• 2.3 0,6
• 2.4 0,8

2.5 0,8

2.6 0,25

3. 0,33333

4.

• 0,333
• 0,666

Test your progress

1.1 442

1.2 17

2. one and one-tenth or 1,1 sausage rolls

3. one and two-tenths or 1 and a fifth sausage rolls (or 1,2)

4. two and a quarter mugs

• 6 x 10 + 4 x 1 + 8 x 0,1
• 3 x 100 + 4 x 10 + 1 x 1 + 2 x 0,1

• 3,8
• 1,3
• 5,25
• 4,5

• <
• <

• 46
• 9,9