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If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal

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If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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New post 02 Mar 2012, 04:20
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A
B
C
D
E

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Question Stats:

56% (01:18) correct 44% (01:32) wrong based on 1069 sessions

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If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal, how many nonzero digits will d have?

A. One
B. Two
C. Three
D. Seven
E. Ten
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Re: d=?  [#permalink]

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New post 02 Mar 2012, 04:29
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wizard wrote:
If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal, how many nonzero digits will d have?

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


Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.
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Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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New post 02 Mar 2012, 05:31
1/2^3*5^7=1/10^3*1/5^4=10^(-3)*0.2^4

2^4=4^2 =16
so ,the answer is -two
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Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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New post 03 Mar 2016, 05:44
Bunuel wrote:
wizard wrote:
If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal, how many nonzero digits will d have?

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


Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.


I thought loosely about this when I solved it.
But I thought it was gonna change the value.
But that does nothing to the ratio. I didn't think hard.
U just check Buñuel's solution if want the smartest detailed solution.
take kudos
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Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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New post 16 Aug 2017, 20:59
1/5=0.2
2⁻³*5⁻³*0.2⁴
now 0.2⁴=0.0016
Hence 2 non zero nos.
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Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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New post 15 Nov 2018, 23:32
1
We are given:

\(d=\frac{1}{(2^3\times 5^7 )}\)


In the denominator, we have two numbers with different bases and different exponents. We can rewrite those numbers to have same exponents.

\(d=\frac{1}{(2^3 \times 5^7 )} \times \frac{2^4}{2^4} =\frac{2^4}{(2^7*5^7 )}\)

\(d=\frac{2^4}{(2\times 5)^7}\)

\(d=\frac{2^4}{10^7}\)


\(2^4 = 16\) and \(10^7\) gives us \(7\) decimal places. We can write this as:

\(0.0000016\)


We have 2 non-zero digits. The final answer is .
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Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal   [#permalink] 15 Nov 2018, 23:32
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