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

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VP
Joined: 09 Mar 2016
Posts: 1284
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

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31 Dec 2017, 05:12
[/quote]

Frankly, the red part does not make any sense...

The denominator is $$2^7*5^7$$. Multiply it by $$2^4$$. What do you get?[/quote]

Hello Bunuel, i have the same question: based on which rule are you multiplying (2^3*5^7) by 2^4 but still ignoring 5^7 ? please help me to understand your smart solution and to answer your question: if multiply (2^3*5^7) by 2^4 I get 2^7 *10^11 Thanks!
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If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

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31 Dec 2017, 07:24
1
dave13 wrote:

Frankly, the red part does not make any sense...

The denominator is $$2^7*5^7$$. Multiply it by $$2^4$$. What do you get?[/quote]

Hello Bunuel, i have the same question: based on which rule are you multiplying (2^3*5^7) by 2^4 but still ignoring 5^7 ? please help me to understand your smart solution and to answer your question: if multiply (2^3*5^7) by 2^4 I get 2^7 *10^11 Thanks![/quote]

Hi dave13

Properties of exponents say that if base is equal then on multiplying you add the powers and on dividing you subtract the powers

i.e. $$a^b*c^d$$ if multiplied by $$a^x$$, then it will become $$a^{(b+x)}*c^d$$, here there will be no impact on $$c^d$$ which has a different base.

In this problem as $$5^7$$ has a power of $$7$$ so we need to make $$2^3$$ as $$2^7$$, hence we multiply the numerator & denominator by $$2^4$$

so $$2^3*5^7*2^4=2^{(3+4)}*5^7=2^7*5^7=(2*5)^7=10^7$$
Intern
Joined: 11 Sep 2017
Posts: 18
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

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31 Dec 2017, 13:08
ilovefrankee wrote:
(First ever post!)

I realise I'm a little late submitting my answer here, but my answer was 2 non-zero digits: 2 & 5.

My answer is based on the following:

1 / (2^3*5^7) = 1 / (2*(2^2))*(5^7) =
1 / (4x10^7) =
25 x 10^8 .

I'm guessing my mistake was in factoring the denominator, specifically factoring of 2^3 as 2x2^2?

Any input greatly appreciated,

Ben

EDIT:

Not to worry, I've gone over some other exponent materials and came up with the correct solution.

Hi Ben,

I'd like to highlight a few things-

1. The two non zero digits are ONE and SIX and not 2 & 5.

2. In your manipulation of the expression, notice that you have missed out a TWO in the 3rd step (1 / (2*(2^2))*(5^7) =
1 / (4x10^7) and where did you get that TEN (1 / (2*(2^2))*(5^7) =
1 / (4x10^7)) from?

Correct manipulation will be: 1 / (2^3*5^7) = 1 / (2^3*5^7) * 2^4/ 2^4 = 2^4/ 10^7 = 16/ 10^7 = 0.0000016. Hence, the two non zero digits are 1 and 6.

Hope this helps.

Aiena.
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Joined: 09 Mar 2016
Posts: 1284
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

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02 Jan 2018, 02:58
niks18 wrote:
dave13 wrote:

Frankly, the red part does not make any sense...

The denominator is $$2^7*5^7$$. Multiply it by $$2^4$$. What do you get?

Hello Bunuel, i have the same question: based on which rule are you multiplying (2^3*5^7) by 2^4 but still ignoring 5^7 ? please help me to understand your smart solution and to answer your question: if multiply (2^3*5^7) by 2^4 I get 2^7 *10^11 Thanks![/quote]

Hi dave13

Properties of exponents say that if base is equal then on multiplying you add the powers and on dividing you subtract the powers

i.e. $$a^b*c^d$$ if multiplied by $$a^x$$, then it will become $$a^{(b+x)}*c^d$$, here there will be no impact on $$c^d$$ which has a different base.

In this problem as $$5^7$$ has a power of $$7$$ so we need to make $$2^3$$ as $$2^7$$, hence we multiply the numerator & denominator by $$2^4$$

so $$2^3*5^7*2^4=2^{(3+4)}*5^7=2^7*5^7=(2*5)^7=10^7$$[/quote]

Thanks a lot niks18 for a detailed explanation. Highly appreciated!
Manager
Joined: 13 Feb 2018
Posts: 156
GMAT 1: 640 Q48 V28
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

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23 Oct 2018, 05:04
Here is my approach:

$$\frac{1}{2^3*5^7}$$=$$\frac{1}{2^3*5^3}$$*$$\frac{1}{5^4}$$=$$\frac{1}{2^3*5^3}$$*$$\frac{1}{5^2}$$*$$\frac{1}{5^2}$$=$$\frac{1}{1000}$$*0.04*0.04
As we were asked for nonzero digits I calculated only 0.04*0.04= 0.0016

d will have only 2 nonzero digits
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how   [#permalink] 23 Oct 2018, 05:04

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