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# If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =

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Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b = [#permalink]
Bunuel wrote:
If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

solve for expression

$$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$
we get
10^a-b = 10^6
a-b= 6
IMO B
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Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b = [#permalink]
Bunuel wrote:
If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

If we re-express 0.036 as 36 x 10^-3 in the numerator and 0.09 as 9 x 10^-2 in the denominator, we obtain:

(36 x 10^-3 x 10^a)/(9 x 10^-2 x 10^b

Simplifying, we have:

(36 x 10^(a-3))/(9 x 10^(b-2)) = 4 x 10^5

36 x 10^(a-3) = (4 x 10^5)(9 x 10^(b-2))

36 x 10^(a-3) = 9 x 4 x 10^(5 + b - 2)

10^(a-3) = 10^(5 + b - 2)

a - 3 = 5 + b - 2

a - b = 6