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# What is the decimal equivalent of (2/5)^5 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59039
What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 01:49
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Difficulty:

35% (medium)

Question Stats:

69% (01:17) correct 31% (01:03) wrong based on 88 sessions

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What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

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Joined: 09 Apr 2018
Posts: 13
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 01:57
1
(2/5)^5 can be written as (4/10)^5

Which is:

2^10
100000

Intern
Joined: 08 Jan 2017
Posts: 21
Location: India
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GMAT 2: 670 Q48 V34
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What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 02:00
1
On multiplying numerator and denominator by 2^5:
(2/5)^5 * (2/2)^5
We get numerator as = 2^10
denominator as = (2*5)^5

2^10 = 1024
(2*5)^5 = 10 ^5

Ans: 0.01024

Tip: Always try to convert denominator as multiple of 10.
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Joined: 16 Oct 2016
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Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 02:02
1
=(2/5)^{5}
=(4/10)^{5}
=4^{5}/10^{5}
=1024/10^{5}
=0.01024
Math Expert
Joined: 02 Sep 2009
Posts: 59039
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 01:50
Bunuel wrote:
What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

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Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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07 Mar 2019, 01:54
Bunuel wrote:
What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

Given,

$$(\frac{2}{5})^5$$

= $$(0.4)^5$$

= (0.4) (0.4) (0.4) (0.4) (0.4) (0.4)

=0.01024.

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Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

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09 Mar 2019, 14:40
Some good explanation above.
I will throw another idea out there-

We know we can write the term as $$(\frac{4}{10}) ^5$$

Which means $$(\frac{4*4*4*4*4}{100000})$$

Cyclicity of 4 is 2. Meaning- If you keep multiplying 4 by 4, the units digits keep changing between 6 and 4. Since the power is 5 it's cyclicity is 2m+1 which tells us the unit's digit will be 4.
Or you can just multiple 4 to itself 5 times in your head (keeping track of just the unit's digit- 4*4 = 16 ; 6*4 = 24; 4*4 = 16 ; 6*4 = 24 ) Unit's digit is 4.

Option E is the only option with unit's digit 4.
Re: What is the decimal equivalent of (2/5)^5 ?   [#permalink] 09 Mar 2019, 14:40
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