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

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Intern
Joined: 17 Oct 2011
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Location: Taiwan
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If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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02 Mar 2012, 04:20
4
59
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Difficulty:

55% (hard)

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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Joined: 02 Sep 2009
Posts: 55668

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02 Mar 2012, 04:29
28
20
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.

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

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

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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.

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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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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Joined: 15 Sep 2018
Posts: 30
Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal  [#permalink]

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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 .
Re: If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal   [#permalink] 15 Nov 2018, 23:32
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