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I am looking for an approach to determine if a fraction has [#permalink]
24 Sep 2008, 10:14

1

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I am looking for an approach to determine if a fraction has a terminating decimal or not without calculating it, for example: which of the following has decimal equivalent to terminating decimal:

I am looking for an approach to determine if a fraction has a terminating decimal or not without calculating it, for example: which of the following has decimal equivalent to terminating decimal:

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

the correct answer is E?

If the denominator can be written in terms of only 2^x*5^y or 2^x or 5^y. Then the fraction is terminating. Here (E) is 2^7 and meets the above condition and hence terminating. _________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

I am looking for an approach to determine if a fraction has a terminating decimal or not without calculating it, for example: which of the following has decimal equivalent to terminating decimal:

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

the correct answer is E?

You need to prime factorize the denominator. If the denominator's prime factors are only 2 and/or 5, then the fraction is a terminating decimal

I am looking for an approach to determine if a fraction has a terminating decimal or not without calculating it, for example: which of the following has decimal equivalent to terminating decimal:

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

the correct answer is E?

You need to prime factorize the denominator. If the denominator's prime factors are only 2 and/or 5, then the fraction is a terminating decimal

I am looking for an approach to determine if a fraction has a terminating decimal or not without calculating it, for example: which of the following has decimal equivalent to terminating decimal:

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

the correct answer is E?

You need to prime factorize the denominator. If the denominator's prime factors are only 2 and/or 5, then the fraction is a terminating decimal

I'd just add one thing here: you *must* make sure that your fraction is reduced before you apply this test. It's not important in the above question, because all of the fractions are already reduced, but it could be important in a different question. For example, you might see:

51/300

and if you just steam ahead and prime factorize that denominator, you'll get 3*2^2*5^2, which might make you think that it's not a terminating decimal. It is, however; when you reduce the fraction, the 3 in the denominator disappears:

51/300 = 17/100 = 0.17 _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

I'd just add one thing here: you *must* make sure that your fraction is reduced before you apply this test. It's not important in the above question, because all of the fractions are already reduced, but it could be important in a different question. For example, you might see:

51/300

and if you just steam ahead and prime factorize that denominator, you'll get 3*2^2*5^2, which might make you think that it's not a terminating decimal. It is, however; when you reduce the fraction, the 3 in the denominator disappears:

51/300 = 17/100 = 0.17

Good point IanStewart. I'd like to add one more thing..... On a reduced fraction, when you see denominators like 300, 234, etc... which shows that the number is divisible by another number other than 2 and 5, you can toss it... this speeds up the process a little. _________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

I'd just add one thing here: you *must* make sure that your fraction is reduced before you apply this test. It's not important in the above question, because all of the fractions are already reduced, but it could be important in a different question. For example, you might see:

51/300

and if you just steam ahead and prime factorize that denominator, you'll get 3*2^2*5^2, which might make you think that it's not a terminating decimal. It is, however; when you reduce the fraction, the 3 in the denominator disappears:

51/300 = 17/100 = 0.17

Good point IanStewart. I'd like to add one more thing..... On a reduced fraction, when you see denominators like 300, 234, etc... which shows that the number is divisible by another number other than 2 and 5, you can toss it... this speeds up the process a little.