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Re: PS: Number property [#permalink]
23 Aug 2009, 07:27

1

This post received KUDOS

I do not think you have to calculate a lot here. The rule is that the fraction terminates if the denominator has ONLY 2 or/and 5 in its prime factorization.

A 10/189...no common factors can be canceled out, and 189 is divisible by 3. The denominator does not have ONLY 2's and 5's since it has 3 in it as well. You can stop here, concluding the fraction does not terminate... B 15/196 - no common factors can be canceled out. 196=2*2*7*7...there is a prime number 7...so the fraction does not terminate.. C 16/225...no common factors can be caceled out. decomposing the denominator 225=25*9=5^2*3^2. Does not terminate since it has 3 in its denominator D 25/144 no common factors can be canceled out. 144= 2*72, and 72 is divisible by 3...so the fraction has 3 in its denominator...does not terminate. E you do not have to check. you know it should be E since it is your last option. But if you want to be sure decompose the denominator and you will get only 2's in it

Re: PS: Number property [#permalink]
07 Sep 2010, 01:37

E. Great question. Be suspicious about 3,7 (more suspicious if the numerator has a factor of 3 or 7). Do not blindly select the answer if the denominator alone has a 3 or 7. If it is 8,4,2,6 then they are usually terminating.

Re: PS: Number property [#permalink]
07 Sep 2010, 04:30

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Expert's post

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TriColor wrote:

Please, explain your answer. Thank you, -----------------------------------------

Q15: 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

THEORY:

Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be terminating decimal.

(We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.)

the necessary and sufficient condition of terminating decimals is that the denominator's prime factors should only be 2 or 5 or both (form \(2^x * 5^y\)) _________________

Re: Which of the following fractions has a decimal equivalent th [#permalink]
18 Jan 2015, 02:49

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