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# Which of the following fractions has a decimal equivalent

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Which of the following fractions has a decimal equivalent [#permalink]  03 Jan 2009, 11:58
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!
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Re: Easier way to find a terminating decimal? [#permalink]  03 Jan 2009, 12:46
UnknownPhD wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

look for denometer that has 2 and/or 5 as prime factor(s).

A. 10/189 = 2x5/(3x3x3x7) ------ 7?
B. 15/196 = 3x5/(2x2x2x2x3x3) ---- 3?
C. 16/225 = 2x2x2x2/(5x5x7) ---- 7?
D. 25/144 = 5x5/(2x2x2x2x3x3) ----3?
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. yes.

So E.
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Re: Easier way to find a terminating decimal? [#permalink]  03 Jan 2009, 13:17
GMAT TIGER wrote:
UnknownPhD wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

look for denometer that has 2 and/or 5 as prime factor(s).

A. 10/189 = 2x5/(3x3x3x7) ------ 7?
B. 15/196 = 3x5/(2x2x2x2x3x3) ---- 3?
C. 16/225 = 2x2x2x2/(5x5x7) ---- 7?
D. 25/144 = 5x5/(2x2x2x2x3x3) ----3?
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. yes.

So E.

hi gmattiger
can you tell me how you decided on E as 2 is the factor in all the answers. also against each answer you have written a number towards the end. what does that mean?

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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 06:50
2
KUDOS
UnknownPhD wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

First, terminating decimals have a fixed number of digits after the decimal point.

For eg. 5/2 = 2.5 (this is a terminating decimal)
1/3 = 1.33333333 ( this is recurring decimal)

For a fraction to have terminating decimals, it can have only 2 and/or 5 as prime factors in the denominator ....

If we see all the denominators, we have prime factors other than 2 and 5. Only choice E has only prime factor as 2

A. 10/189 = 2x5/(3x3x3x7) ..... This has 3 and 7. So this will definitely have recurring decimals.
B. 15/196 = 3x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.
C. 16/225 = 2x2x2x2/(5x5x7) ..... This has 5 but this also has 7 which means this will definitely have recurring decimals.
D. 25/144 = 5x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. This has ONLY 2. So this HAS to be a terminating decimal

Choice E has to be the right answer.

Hope this helped. If not, let me know.
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Manager
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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 07:51
amitdgr wrote:
UnknownPhD wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

First, terminating decimals have a fixed number of digits after the decimal point.

For eg. 5/2 = 2.5 (this is a terminating decimal)
1/3 = 1.33333333 ( this is recurring decimal)

For a fraction to have terminating decimals, it can have only 2 and/or 5 as prime factors in the denominator ....

If we see all the denominators, we have prime factors other than 2 and 5. Only choice E has only prime factor as 2

A. 10/189 = 2x5/(3x3x3x7) ..... This has 3 and 7. So this will definitely have recurring decimals.
B. 15/196 = 3x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.
C. 16/225 = 2x2x2x2/(5x5x7) ..... This has 5 but this also has 7 which means this will definitely have recurring decimals.
D. 25/144 = 5x5/(2x2x2x2x3x3) ..... This has 2 but this also has 3 which means this will definitely have recurring decimals.
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. This has ONLY 2. So this HAS to be a terminating decimal

Choice E has to be the right answer.

Hope this helped. If not, let me know.

Thanks a lot. this is a good tip.
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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 10:38
1
KUDOS
ALD wrote:
GMAT TIGER wrote:
UnknownPhD wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

look for denometer that has 2 and/or 5 as prime factor(s).

A. 10/189 = 2x5/(3x3x3x7) ------ 7?
B. 15/196 = 3x5/(2x2x2x2x3x3) ---- 3?
C. 16/225 = 2x2x2x2/(5x5x7) ---- 7?
D. 25/144 = 5x5/(2x2x2x2x3x3) ----3?
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. yes.

So E.

hi gmattiger
can you tell me how you decided on E as 2 is the factor in all the answers. also against each answer you have written a number towards the end. what does that mean?

The difference between E and any other answer choice is that E has only 2 where as others have 2 or 3 or 7. If the denomenator has 2 or 5 or both, the the fraction is terminating decimal.
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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 16:56
GMAT TIGER wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

look for denometer that has 2 and/or 5 as prime factor(s).

A. 10/189 = 2x5/(3x3x3x7) ------ 7?
B. 15/196 = 3x5/(2x2x2x2x3x3) ---- 3?
C. 16/225 = 2x2x2x2/(5x5x7) ---- 7?
D. 25/144 = 5x5/(2x2x2x2x3x3) ----3?
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. yes.

So E.

hi gmattiger
can you tell me how you decided on E as 2 is the factor in all the answers. also against each answer you have written a number towards the end. what does that mean?

The difference between E and any other answer choice is that E has only 2 where as others have 2 or 3 or 7. If the denomenator has 2 or 5 or both, the the fraction is terminating decimal.

Good trick GMATTiger... until now I use to just calculate it manually... but I am smelling something wrong in this. I guess this needs to be improved a bit. For Ex take the case - 9/18,

here 18 = 2x3X3 but its terminating...

I guess improvement could be on the line that numerator has 2 or not, numerator and denominator are even/odd .. right now I am not able to frame it exactly .. but ya I can solve these questions with your trick now .. Thanks
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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 18:30
Expert's post
mar2hathoda wrote:
GMAT TIGER wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Need to know faster way to find the terminating decimal...thanks!

look for denometer that has 2 and/or 5 as prime factor(s).

A. 10/189 = 2x5/(3x3x3x7) ------ 7?
B. 15/196 = 3x5/(2x2x2x2x3x3) ---- 3?
C. 16/225 = 2x2x2x2/(5x5x7) ---- 7?
D. 25/144 = 5x5/(2x2x2x2x3x3) ----3?
E. 39/128 = 3x13/(2x2x2x2x2x2x2) -----2. yes.

So E.

hi gmattiger
can you tell me how you decided on E as 2 is the factor in all the answers. also against each answer you have written a number towards the end. what does that mean?

The difference between E and any other answer choice is that E has only 2 where as others have 2 or 3 or 7. If the denomenator has 2 or 5 or both, the the fraction is terminating decimal.

Good trick GMATTiger... until now I use to just calculate it manually... but I am smelling something wrong in this. I guess this needs to be improved a bit. For Ex take the case - 9/18,

here 18 = 2x3X3 but its terminating...

I guess improvement could be on the line that numerator has 2 or not, numerator and denominator are even/odd .. right now I am not able to frame it exactly .. but ya I can solve these questions with your trick now .. Thanks

You need to reduce your fractions first. I explained all of this in detail on another forum:

www.beatthegmat.com/terminating-decimal-t11910.html
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Re: Easier way to find a terminating decimal? [#permalink]  04 Jan 2009, 21:28
mar2hathoda wrote:
Good trick GMATTiger... until now I use to just calculate it manually... but I am smelling something wrong in this. I guess this needs to be improved a bit. For Ex take the case - 9/18,

here 18 = 2x3X3 but its terminating...

I guess improvement could be on the line that numerator has 2 or not, numerator and denominator are even/odd .. right now I am not able to frame it exactly .. but ya I can solve these questions with your trick now .. Thanks

9/18 cannot be an option. It is in fact 1/2, which has 2 in denominator..
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Re: Easier way to find a terminating decimal?   [#permalink] 04 Jan 2009, 21:28
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