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3.2 Multiplying and dividing by powers of 10

) Exercise 3.2

1 Work these out.
a 13 × 10 b 7.8 × 10 c 24 × 10 d 8.55 × 10 4 Remember:
3
2
e 6.5 × 10 f 0.08 × 10 g 17 × 10 h 8 × 10 −1 10 = 1
0
0
1
5
i 8.5 × 10 j 4500 × 10 k 32 × 10 l 125 × 10 −2 10 = 10
−3
−2
−4
1
2 Work these out.
a 27 ÷ 10 b 450 ÷ 10 c 36 ÷ 10 d 170 ÷ 10 4
2
3
e 0.8 ÷ 10 f 2480 ÷ 10 g 9 ÷ 10 h 0.25 ÷ 10 −1
1
0
5
i 18 ÷ 10 j 4.76 ÷ 10 k 0.07 ÷ 10 l 0.085 ÷ 10 −2
−2
−3
−4
3 Copy this table, which contains a secret coded message.
S !
3 3.3 0.3 3.3 300 300 33 6 6 0.6 0.3 0.33 3.3 0.3 33 300 0.06 33 60 33 0.03 600 33 300
Work out the answers to the calculations in the code
2
−1
box on the right. 0.6 × 10 = S 60 × 10 = L
0
−1
Find the answer in your secret code table. Write the 0.06 ÷ 10 = A 600 ÷ 10 = R
letter from the code box above the number in your table. 60 × 10 = H 33 ÷ 10 = O
1
−3

2
For example, the first calculation is 0.6 × 10 . 0.33 × 10 = Y 300 × 10 = N
−3
0
0.6 × 10 = 60, so write S above 60 in the table.
2
−2
4
What is the secret coded message? 300 ÷ 10 = C 3300 × 10 = E
0.3 ÷ 10 = T 300 ÷ 10 = D
−3
2
4 Work out the missing power in each of the questions in these spider diagrams.
In each part, all the questions in the outer shapes should give the answer in the centre shape.
a b
0.8 × 10 8 ÷ 10 32 ÷ 10 0.32 × 10 These are
called spider
80 × 10 = 8 0.08 ÷ 10 3.2 ÷ 10 = 0.32 320 ÷ 10 diagrams
because they
0.008 × 10 800 ÷ 10 32 × 10 3.2 × 10 have a central
‘body’ with
several ‘legs’.
5 a Work these out.
0
2
i 4 × 10 ii 4 × 10 iii 4 × 10 iv 4 × 10 v 4 × 10 vi 4 × 10 −3
−2
−1
1
b Use your answers to part a to answer this question.
If you multiply a number by 10 , would the answer be larger or smaller than when you multiply
−4
−3
the same number by 10 ?
6 a Work these out.
2
i 12 ÷ 10 ii 12 ÷ 10 iii 12 ÷ 10 iv 12 ÷ 10 v 12 ÷ 10 vi 12 ÷ 10 −3
1
−2
−1
0
b Use your answers to part a to answer this question.
If you divide a number by 10 , would the answer be larger or smaller than when you divide the
−4
−3
number by 10 ?
3 Place value, ordering and rounding 27