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# If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct

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If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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sony1000 wrote:
If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct nonzero digits will x have?

A. One
B. Two
C. Three
D. Seven
E. Ten

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Hope it helps.
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Re: If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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sony1000 wrote:
If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct nonzero digits will x have?

A. One
B. Two
C. Three
D. Seven
E. Ten

we try to make dominator the multiple of 10,
so we multiple with 5^4

we have 5^4/9, we do not care how many 10 factors are there is the dominator

divide
694444444

so, there is only 3 distict

tricky
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Re: If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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sony1000 wrote:
If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct nonzero digits will x have?

A. One
B. Two
C. Three
D. Seven
E. Ten

Following is the simple calculation.

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If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
Took 01:02.

1st) do some fast math in your head: 4*9*16*25 = 64 * 225 = 10* 225 + 50* 225 + 4 * 225 = 2250 + 50*200 + 50*25 + 900 = 12250 + 1250 + 900 = 14 400 (or: 100*16*10 - 1600 = 16000 - 1600 = 14400)
2nd) switch the fraction into a decimal
done

the easy way.
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Re: If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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I used indices to solve this question.

Multiplying the denominator;

x = $$\frac{1}{2^2*3^2*4^2*5^2}$$

x = 1/120^2

(i got 120 by multiplying 2*3*4*5)

x = $$\frac{1}{(12*10)^2}$$

x = $$\frac{1}{144*100}$$

x = $$\frac{1}{14400}$$

three distinct numbers!

Let me know if this method is sound. Thanks

Give me kudos if you like my explanation
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Re: If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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Re: If x= 1/(2^2*3^2*4^2*5^2) is expressed as a decimal, how many distinct [#permalink]
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