Page 17 - 新思维数学学生用书9 样章

1 Number and calculation

3 Write these numbers as powers of 2.

a 1 b 1 c 64
2 4
d 64 e 1 f 8 −1
1
4 Write each number as a power of 10.
a 100 b 1000 c 1
d 0.1 e 0.001 f 0.000 001

5 Write 1
64
a as a power of 64 b as a power of 8
c as a power of 4 d as a power of 2.

6 a Write 1 as a power of a positive integer.
81
b How many different ways can you write the answer to part a?

7 When x = 6, find the value of
a x 2 b x −2 c x 0 d x .
−3
8 Write m as a fraction when
−2
a m = 9 b m = 15 c m = 1 d m = 20.

9 y = x + x and x is a positive number.
−2
2
a Write y as a mixed number when
i x = 1 ii x = 2 iii x = 3.
b Find the value of x when

i y = 25.04 ii y = 100.01.
10 a Write the answer to each multiplication as a power of 3.
i 3 × 3 3 ii 3 × 3 5
2
4
×
6
iii 3 × 3 4 iv 3 3 5
b In part a you used the rule 3 × 3 = 3 ab when the indices are positive integers.
+
b
a
In the following multiplications, a or b can be negative integers.
Show that the rule still gives the correct answers.
−
i 3 × 3 − 1 ii 3 × 3 Tip
2
2
−
3
1
iii 3 × 3 − 1 iv 3 × 3 − 1 Write out the
−
v 3 × 3 − 1 numbers and
2
c Write two examples of your own to show that the rule works. multiply.
d Give your work to a partner to check.
11 Write the answer to each multiplication as a power of 5.
a 5 × 5 2 b 5 × 5 − 2
4
4
c 5 × 5 2 d 5 × 5 − 2
−
−
4
4

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