Section 2.2 ­ Powers of ten and the zero exponent
75 7 x 7 x 7 x 7 x 7 16807
74 7 x 7 x 7 x 7 2401
73 7 x 7 x 7 343
0
72 7 x 7 49
71 7 7
70 ? ?
Decreasing powers of 10
1
We can make a similar table for the powers of any integer base except 0
1 can be written as any power without the exception of 0
1 = 2
0
1 = 13
0
1 = (­4)
0
Zero exponent law:
A power with exponent 0 is equal to 1
60 = 1
(­5)0 = 1 ** The zero exponent applies to the number in the brackets only.
80 = 1
­40 = ­1 ** If there are no brackets, the zero exponent applies only to the base.
(­10)0 = 1
­(­9)0 = ­1
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Powers of ten:
10 000 written as a power of 10 104
100 000 105
10 101
1 100
The exponent is equal to the number of zeros
Writing numbers using Powers of ten
write 3452 using powers of ten
3452 is written in standard form
When it is written using powers of ten, it is written in expanded form
3452 = (3 x 1000) + (4 x 100) + (5 x 10) + (2 x 1)
= (3 x 103) + (4 x 102) + (5 x 101) + (2 x 100)
76359 = (7 x 10000) + (6 x 1000) + (3 x 100) + (5 x 10) + (9 x 1)
= (7 x 104) + (6 x 103) + (3 x 102) + (5 x 101) + (9 x 100)
3
600
= (6 x 100)
= (6 x 102)
4300 = (4 x 1000) + (3 x 100)
= (4 x 103) + (3 x 102)
100 000
= (1 x 100 000)
= (1 x 105)
3 000 000 = (3 x 1 000 000)
= (3 x 106)
Practice page 61 4 ­ 13
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