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Difficulty: Sub 505 Level,    Arithmetic,    Fractions and Ratios,                            
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Re: 31/125 = [#permalink]
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\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320


\(\frac{31}{125} = \frac{31*8}{125*8} = \frac{248}{1000} = 0.248\)

Answer: (A)
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Re: 31/125 = [#permalink]
125 can simply be written as 1000/8
multiply 8 with 31 to get 248
divide it by 1000 to get .248
answer is A
simple one
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Re: 31/125 = [#permalink]
Bunuel wrote:
SOLUTION

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

\(\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248\).

Answer: A.

why do you choose to times by 8?
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Re: 31/125 = [#permalink]
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sabxu1 wrote:
Bunuel wrote:
SOLUTION

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

\(\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248\).

Answer: A.

why do you choose to times by 8?


The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.
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Re: 31/125 = [#permalink]
Bunuel wrote:
sabxu1 wrote:
Bunuel wrote:
SOLUTION

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

\(\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248\).

Answer: A.

why do you choose to times by 8?


The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.


do you times i by 8 because you want to get to an easy number such as 1000?
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Re: 31/125 = [#permalink]
Expert Reply
sabxu1 wrote:
Bunuel wrote:
sabxu1 wrote:
why do you choose to times by 8?


The options are in decimals. To transform a fraction to decimal the denominator must be some power of 10. 125*8 = 1000.


do you times i by 8 because you want to get to an easy number such as 1000?


As I said, we multiply by 8 to get in the denominator some power of 10 to transform the fraction into the decimal easily.
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Re: 31/125 = [#permalink]
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sabxu1 wrote:
Bunuel wrote:
SOLUTION

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

\(\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248\).

Answer: A.

why do you choose to times by 8?


Since the options are all in the decimal forms, we need to divide the numerator by denominator.
If we have a calculator, we can directly divide it. But since we are not allowed a calculator, we need to make our lives simpler.

Hence we try to bring denominator in a form by which the division becomes easier.
125 = 5^3
If we multiply 5^3 by 2^3, we get 10^3 or 1000 and then we can easily divide.

Hope this clarifies your doubt.
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Re: 31/125 = [#permalink]
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Bunuel wrote:
\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320


\(\frac{31}{125}\)

\(~ \frac{31}{124}\)

\(=\frac{1}{4}\)

\(=0.25\)

Thus, answer will be (A) 0.248
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Re: 31/125 = [#permalink]
In case someone is interested in a more detailed approach.

\(\frac{31}{125} = \frac{30}{125}+\frac{1}{125} \\
\\
= \frac{6}{25}+\frac{1}{125} \\
\\
= \frac{5}{25} + \frac{1}{25} + \frac{1}{125} \\
\\
= \frac{1}{5}+ \frac{1}{25} + \frac{1}{125}\)

\(= 0.2 + \frac{0.2}{5}+ \frac{1}{125} = 0.2 +0.04 + \frac{1}{125} = 0.24 + \frac{1}{125}\)

= a little over 0.24

= Option A
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Re: 31/125 = [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

Problem Solving
Question: 58
Category: Arithmetic Operations on rational numbers
Page: 69
Difficulty: 500


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\(\frac{31}{125}\)

Or, \(\frac{31}{124}=\frac{1}{4} = 0.25\)

Since we have approximated 125 as 124, 0.25 will be slightly less than 0.25 ie, 0.248, Answer must be (A)
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Re: 31/125 = [#permalink]
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