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

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Joined: 02 Sep 2009
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Which of the following when expressed as a decimal has a finite number  [#permalink]

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14 Jan 2018, 06:17
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45% (medium)

Question Stats:

62% (02:20) correct 38% (02:04) wrong based on 46 sessions

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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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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. $$\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9$$

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

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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. $$\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9$$

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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