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Which of the following when expressed as a decimal has a finite number

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Which of the following when expressed as a decimal has a finite number [#permalink]

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New post 14 Jan 2018, 06:17
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Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. \(\frac{0.27^3}{0.09^4}\)

B. \(\frac{0.27^2}{0.09^8}\)

C. \(\frac{27^3}{0.09^6}\)

D. \(\frac{0.27^3}{0.09^5}\)

E. \(\frac{0.27^3}{0.09^9}\)

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Which of the following when expressed as a decimal has a finite number [#permalink]

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New post 14 Jan 2018, 06:45
Bunuel wrote:
Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. \(\frac{0.27^3}{0.09^4}\)

B. \(\frac{0.27^2}{0.09^8}\)

C. \(\frac{27^3}{0.09^6}\)

D. \(\frac{0.27^3}{0.09^5}\)

E. \(\frac{0.27^3}{0.09^9}\)



RULE: A number will always be NON-TERMINATING if the denominator of fraction in least form has any prime factor other than 2 and 5

i.e. RULE: A number will always be TERMINATING if the denominator of fraction in least form has NO prime factor other than 2 and 5

A. \(\frac{0.27^3}{0.09^4} = 27^3/9^4 = 3^9/3^8 = 3\) CORRECT ANSWER

B. \(\frac{0.27^2}{0.09^8} = 27^2/9^8 = 3^6/3^16 = 1/3^10\)

C. \(\frac{27^3}{0.09^6} = 27^3/9^6 = 3^9/3^12 = 1/3^3\)

D. \(\frac{0.27^3}{0.09^5} = 27^3/9^4 = 3^9/3^10 = 1/3\)

E. \(\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9\)

Answer: Option A
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Re: Which of the following when expressed as a decimal has a finite number [#permalink]

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New post 23 Jan 2018, 02:57
GMATinsight wrote:
Bunuel wrote:
Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. \(\frac{0.27^3}{0.09^4}\)

B. \(\frac{0.27^2}{0.09^8}\)

C. \(\frac{27^3}{0.09^6}\)

D. \(\frac{0.27^3}{0.09^5}\)

E. \(\frac{0.27^3}{0.09^9}\)



RULE: A number will always be NON-TERMINATING if the denominator of fraction in least form has any prime factor other than 2 and 5

i.e. RULE: A number will always be TERMINATING if the denominator of fraction in least form has NO prime factor other than 2 and 5

A. \(\frac{0.27^3}{0.09^4} = 27^3/9^4 = 3^9/3^8 = 3\) CORRECT ANSWER

B. \(\frac{0.27^2}{0.09^8} = 27^2/9^8 = 3^6/3^16 = 1/3^10\)

C. \(\frac{27^3}{0.09^6} = 27^3/9^6 = 3^9/3^12 = 1/3^3\)

D. \(\frac{0.27^3}{0.09^5} = 27^3/9^4 = 3^9/3^10 = 1/3\)

E. \(\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9\)

Answer: Option A


Dear GMATINSIGHTS,
Can you please explain to me in detail how you eliminate the 10^-2? Thanks a LOT!
Re: Which of the following when expressed as a decimal has a finite number   [#permalink] 23 Jan 2018, 02:57
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Which of the following when expressed as a decimal has a finite number

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