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If X = 625,000, how many nonzero digits are in the decimal representat 29 Mar 2018, 23:53
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35% (medium)

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67% (01:35) correct 33% (01:30) wrong based on 99 sessions

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If X = 625,000, how many nonzero digits are in the decimal representation of 1/X ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five
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B
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If X = 625,000, how many nonzero digits are in the decimal representat 30 Mar 2018, 00:01
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Bunuel
If X = 625,000, how many nonzero digits are in the decimal representation of 1/X ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

1/625000 = 1/1000 x 1/625 = 0.001 x 0.0016

2 non zero digits
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If X = 625,000, how many nonzero digits are in the decimal representat 31 Mar 2018, 11:18
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Bunuel
If X = 625,000, how many nonzero digits are in the decimal representation of 1/X ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

I have a tendency to do these calculations mentally.
Here is how I solved it mentally-

625,000= \(5^4*1000\)
1000 wont effect the non zero digits.
1/625 will have the same digits as 1/625,000
\(1/5^4\)=\(0.2^4\)=0.0016
Hence answer is 2 non zero digits- B
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If X = 625,000, how many nonzero digits are in the decimal representat 31 Mar 2018, 11:18
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Bunuel
If X = 625,000, how many nonzero digits are in the decimal representation of 1/X ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five
One easy method: multiply both numerator and denominator by \(\frac{a^{b}}{a^{b}}\) to create only powers of 10 in the denominator.
Division by 10 changes the decimal position, not the number of non-zero digits in the numerator.

Find the prime factors of 625,000
\(625,000 = (625 * 1,000) =\)
\((5^4*10^3)=(5^4*5^32^3)\)

\(\frac{1}{X}=\frac{1}{625,000}=\frac{1}{(5^4*5^32^3)}\)

There are seven powers of 5, but only three powers of 2. We want only powers of 10 in the denominator. We need four more 2s

\(\frac{1}{(5^45^32^3)}*(\frac{2^4}{2^4})=(\frac{2^4}{10^7})\)
\(2^4 = 16\)

There will be TWO non-zero digits in the decimal representation.

Answer B

(The number is .0000016)
Edit: Digvijay101 , simultaneous post. No wonder my browser got stuck. :-)
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If X = 625,000, how many nonzero digits are in the decimal representat 20 Apr 2022, 07:01
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