Introduction to Decimals for Functional Maths, Adult Numeracy, Common Entrance, 11-plus.

1. Decimals
www.primemaths.co.uk

2. What are Decimals?
Fraction Part
(four tenths)
7.4
Whole Number - 7
1 decimal place
Decimal Point .
(1dp)
Everyday use of decimals: Money
£3.24 = 324p ; 100p = £1 or 1p = 1
100
(1 hundredth of a Pound)
Wrong!!
Note that £1.27 or 127p Not £1.27p
www.primemaths.co.uk 2

3. Recall Conversions
1
• 10 mm = 1 cm, 1 mm = 10 cm or 0.1 cm
• 100 cm = 1 m
1
• 1 cm = 100 m or 0.01 m
1
• 1p = £ 100 = £0.01
• 1 kg = 1000g; 1km = 1000m, 1 l = 1000 ml
www.primemaths.co.uk 3

4. Place Value for Decimals
Thirty two point 10ths 100ths 1000ths
HTU .
zero zero six
32 . 0 0 6
Point zero two . 0 2 7
seven or
333 . 3 3
Zero point zero
two seven
Three hundred and thirty three point three three
www.primemaths.co.uk 4

5. Money
Parts of a £ [pence]
Pounds .
10th of £ [10p] 100ths of £ [1p]
H T U .
3 3 3 . 3 3
Three hundred and thirty three pounds and thirty three pence
£333.33
www.primemaths.co.uk 5

6. Fractions, Decimals, Percentages
Fractions Decimals Percentages
1/20 0.05 5%
1/10 0.1 10%
1/5 0.2 20%
1/4 0.25 25%
1/3 0.33 33.33%
1/2 0.5 50%
2/3 0.67 67%
3/4 0.75 75%
4/5 0.80 80%
1 1.0 100%
www.primemaths.co.uk 6

7. Rounding of Decimals - I
• Round to whole number or whole £
• Look at the 10th unit [1st decimal place]
– If it is below 5, leave the number as it is
– If equal 5 or above, round up by 1
Round 3.48 to nearest whole number
The first decimal place is 4 and its less than
5. So 3.48 is 3 to the nearest whole number
www.primemaths.co.uk 7

8. Rounding of Decimals - II
• Round to one decimal place
• Look at the second decimal place
– If it is below 5, leave the first decimal place as
it is
– If equal 5 or above, round the first decimal
place up
• 3.48 to one decimal place
2nd decimal place is 8, which is more than 5.
So 3.48 to 1dp is 3.5
www.primemaths.co.uk 8

9. Rounding of Decimals - III
• Round to two decimal places
• Look at the third decimal lace
– If it is below 5, leave the second decimal place
as it is
– If equal 5 or above, round the second decimal
place up
• 3.487 to two decimal places
3nd decimal place is 7, which is more than 5.
So 3.487 to 2dp is 3.49
www.primemaths.co.uk 9

10. Rounding of Money - I
• Round to nearest £
• If the amount ends in 50p or more, round up
• If the amount ends in less than 50p, round
down
• £6.48 to the nearest pound
£6.48 to the nearest pound is £6 (48p is less than 50p)
www.primemaths.co.uk 10

11. Rounding of Money - II
• Round to nearest 10p
• If the amount ends in 5p or more, round up
to the next 10p above
• If the amount ends in less than 10p, round
down to the 10p below
• 64p to the nearest 10p
64p to the nearest 10p is 60p (4 is less than 5)
www.primemaths.co.uk 11

12. Addition and Subtraction of Decimals
16.07 + 3.1
1 6 . 0 7
.+ 3 . 1 0
1 9 . 1 7
Line up the
decimal places
22.3 - 3.25
2 2 . 3 0
Fill gaps with 0s
.- 3 . 2 5
1 9 . 0 5
www.primemaths.co.uk 12

13. Multiply decimals by 10 and 100 - I
To multiply by 10 or 100, move the numbers to the left so they
become larger.
Move the numbers as many times as there are zeros, I.e once
for 10 and twice for 100
e.g 3.12 x 10 [ Move one step]
H T U . 10th 100ths
3 . 1 2
3 1 . 2
www.primemaths.co.uk 13

14. Multiply decimals by 10 and 100 - II
e.g 3.12 x 100 [ Move two steps]
H T U . 10th 100ths
3 . 1 2
3 1 2 .
www.primemaths.co.uk 14

15. Multiply decimals
• Approximate first to get an idea of the final amount
•Ignore decimal points
•Count the total number of decimal places in both numbers
•Starting at the end of the answer count the same number of
decimal places and insert the decimal point
•Add zeros to the front if needed
e.g 5.1 x 2.99 = 15.249 [ Multiply 299 x 51 ]
1 dp 2 dp 3 dp (1 dp + 2 dp)
Estimate: 5 x 3 = 15
www.primemaths.co.uk 15

16. Divide decimals by 10 and 100 - I
To divide by 10 or 100, move the numbers to the right so they
become smaller.
Move the numbers as many times as there are zeros, I.e once
for 10 and twice for 100
e.g 31.2 ÷ 10 [ Move one step]
H T U . 10th 100ths
3 1 . 2
3 . 1 2
www.primemaths.co.uk 16

17. Divide decimals by 10 and 100 - II
e.g 312 ÷ 100 [ Move two steps]
H T U . 10th 100ths
3 1 2 .
3 . 1 2
www.primemaths.co.uk 17

18. Divide Decimals by whole number
• Approximate first to get a rough answer
• Ignore decimal points
•Divide as normal
•Keep the decimal points in line
•Compare results with your estimate
e.g 37.24 ÷ 7 =
35 ÷ 7 = 5,
5 . 3 2
7 3 7 . 2 4
www.primemaths.co.uk 18

19. Subscribe to
www.primemaths.co.uk
• 11-plus and Common Entrance Maths Revision
• Adult Numeracy Level 1 and 2 Revision
• Functional Maths Level 1 and 2 Revision
• GCSE Foundation Maths Revision
www.primemaths.co.uk 19