Scientific notation(20點)

2011-08-20 11:28 pm
A number X ,when written in scientific notation is a×10^-6 (where a not = 1).If b×10^n is the scientific notation of 1/X ,then n=?

回答 (1)

2011-08-21 4:36 am
✔ 最佳答案
x = a x 10^-6
1/x =1/( a x 10^-6)
1/x =(1/a) x 10^6

b x 10^n is scientific notation,
b x 10^n = 1/x = (1/a) x 10^6

1/a is less than 1, 0 < 1/a < 1

(1/a) x 10^6 = c x 10^n (1 <= c < 10)

10 (1/a) x 10^5 = c x10^5

n = 5

Check:
Let a = 5
x = 5 x 10^-6
1/x = 1/(5 x 10^-6) = 0.000005 = 5 x 10^5
b = 5
n = 5

2011-08-20 20:42:49 補充:
Sorry, I made a mistake in 1/x = 5 x 10^5

CORRECTION:
Check:
Let a = 5
x = 5 x 10^-6
1/x = 1/(5 x 10^-6) = 200000 = 2 x 10^5
b = 2
n = 5


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