Page 25 - 新思维数学学生用书8 样章

1 Integers

8 Read what Sofia says.

4 is equal to 2 and 4
4
2
3
is equal to 3
4
Is Sofia correct? Give a reason for your answer.
9 A million is 10 . A billion is 1000 million.
6
Write as a power of 10
a one billion b 1000 billion
10 Write in index form
a 2 × 2 × 2 b 3 × 3 × 3 2
4
3
3
2
c 5 × 5 × 5 3 d 10 × 10 × 10 4
3
3
2
11 a (3 ) = 3 × 3 × 3 Write (3 ) as a single power of 3.
2
2
2
2 3
2 3
b Write in index form
i (2 ) ii (5 ) iii (4 )
3 2
2 3
3 2
iv (15 ) v (10 )
4 3
2 4
c N is a positive integer. Write in index form
i (N 23 ii (N 42 iii (N 53
)
)
)
d Can you generalise the results of part c?
Think like a mathematician
12 Here is a division: 32 ÷ 4 = 8
You can write this using indices: 2 ÷ 2 = 2 3
5
2
a Write each of these divisions using indices. All the numbers are powers of
2 or 3.
i 64 4 = 16 ii 81 3÷= 27 iii 512 16 = 32
÷
÷
iv 729 9 = 81 v 99÷ = 1
÷
b Write some similar divisions using powers of 5.
c Can you generalise your results from a and b?
Check with some powers of other positive integers.
d Compare your results with a partner’s.

13 Write the answers to these calculations in index form.
a 2 ÷ 2 5 b 10 ÷ 10 3 c 15 ÷ 15 6
7
8
6
d 8 ÷ 8 9 e 2 ÷ 2 11 f 2 ÷ 2 5
10
15
5
14 Write the answers to these calculations in index form.
a 9 × 9 2 b 9 ÷ 9 2 c (9 ) d 5 × 5 4
5
5
5
5 2
e 12 ÷ 12 3 f (7 ) g (10 04
8
3 3
)
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