Page 41 - MAT KS3 Y8 Cambridge CheckPoint

3.6 Multiplying by decimals

3.6 Multiplying by decimals

When you multiply a number by a decimal, use the Units t tenths hundredths thousandths
decimal place-value table to help you.
1 1 1
If you know the value of the decimal, you can work 1 t 10 100 1000
out an equivalent calculation to complete
(where one calculation can be replaced by another that gives an identical outcome).

Worked example 3.6

Work these out. a 4.37 × 0.3 b 24 × 0.08
3
a (4.37 × 3) ÷ 10 0.3 = , so multiplying by 0.3 is the same as multiplying by 3 and dividing by 10.
10
437 Start by working out 4.37 × 3.
× 3 First of all, ignore the decimal point and work out 437 × 3.
1311
1 2
4.37 × 3 = 13.11 Put the decimal point back into the answer. There are two digits after the decimal
point in the question, so there must be two digits after the decimal point in the
answer.
4.37 × 0.3 = 1.311 The final step is to divide 13.11 by 10, so move all the digits in the number one
place to the right.
8
b (24 × 8) ÷ 100 0.08 = , so multiplying by 0.08 is the same as multiplying by 8 and
100
24
× 8 dividing by 100.
Start by working out 24 × 8.
192
3
24 × 8 = 192
24 × 0.08 = 1.92 The final step is to divide 192 by 100, so move all the digits two places to the right.

✦ Exercise 3.6

1 Use equivalent calculations to work these out.
a 2.48 × 0.2 b 1.76 × 0.3 c 5.22 × 0.4 d 9.27 × 0.5 e 4.18 × 0.06
f 2.9 × 0.07 g 14.6 × 0.08 h 15.1 × 0.09 i 76 × 0.04 j 358 × 0.03

2 This is part of Tanesha’s
homework. Question Work out 24.3 × 0.06.
a Explain why Tanesha’s A A A A A A A 24.3 × 0.06 = (24.3 ÷ 100) × 6 24 3
Answer
method gives the correct 24.3 ÷ 100 = 0.243 × 6
answer. 0.243 × 6 = 1.458 14 5 8
b Use Tanesha’s method to 2 1
work these out.
i 12.2 × 0.07 ii 23.8 × 0.09 iii 1.74 × 0.4 iv 0.67 × 0.8
3 Mia worked out the multiplication 144 × 6 = 864.
Work these out mentally.
a 144 × 0.6 b 1.44 × 0.6 c 14.4 × 0.06 d 0.144 × 0.06

4 Show that 0.6 × 6839.5 kg is approximately 4.1 t. Remind yourself of conversion factors using page 34.
3 Place value, ordering and rounding 39