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

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New post 11 Aug 2019, 05:19
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If \(x\)= \(\frac{1}{2^2*3^2*4^2*5^2}\) 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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New post 11 Aug 2019, 20:14
The number of distinct non zero digit in \(\frac{1}{2^2*3^2*4^2*5^2}\) is equal to that in \(\frac{11111......}{16}\)
\(\frac{11111....}{16}\)=69444......

Option C




SajjadAhmad wrote:
If \(x\)= \(\frac{1}{2^2*3^2*4^2*5^2}\) 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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If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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New post 11 Aug 2019, 21:13
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SajjadAhmad wrote:
If \(x\)= \(\frac{1}{2^2*3^2*4^2*5^2}\) is expressed as a decimal, how many distinct nonzero digits will \(x\) have?


A. One

B. Two

C. Three

D. Seven

E. Ten


Given: \(x\)= \(\frac{1}{2^2*3^2*4^2*5^2}\) is expressed as a decimal.

Asked: How many distinct nonzero digits will x have?

2*3*4*5 = 120
We can multiply the expression by any power of 10 without changing non-zero digits.
\(\frac{1*1000}{120}= \frac{1000}{120} = \frac{25}{3}\)
But expression is \(\frac{1}{120^2}\)
\(\frac{25^2}{3^2} = \frac{625}{9} = 69 \frac{4}{9} = 69.44444...\)
No of unique non-zero digits = 6,9 & 4 (3 unique non-zero numbers)

IMO C
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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New post 21 Aug 2019, 01:49
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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New post 24 Aug 2019, 02:08
It's only 1/144 that matters for the question (not 2 and 5).

What's a quick way to solve this? Are we just meant to know the number of digits?
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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New post 17 Nov 2019, 23:54
\(x=\frac{(1*5^4)}{(3^2*2^4*5^4)}=\frac{625}{90000}=0.00694444...\)
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many   [#permalink] 17 Nov 2019, 23:54
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