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If r and s are positive integers, is r/s a terminating decimal? 03 Jul 2023, 06:00
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If r and s are positive integers, is r/s a terminating decimal?

(1) r is a factor of 100
(2) s is a factor of 500
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B
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If r and s are positive integers, is r/s a terminating decimal? 03 Jul 2023, 07:08
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If r and s are positive integers, is r/s a terminating decimal?

(1) r is a factor of 100
(2) s is a factor of 500
Statement 1:
100= 2^2 X5^2
Since r is a factor of 100, r could be anything. r= 2,5,4,20,25,50,100
No clear information about s . so cancel A and D
Statement 2:
500= 2^2 X5^3
Since s is a factor of 500, s could be anything. s= 2,5,4,20,25,50,100,125,250,500
No clear information about r . so cancel B
Statement 1+2:
r s r/s
2 2 2/2=1 not a terminating decimal
5 2 5/2=2.5 terminating decimal
2 5 2/5=0.4 terminating decimal

Multiple answers, so cancel C
Option E is correct
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If r and s are positive integers, is r/s a terminating decimal? 03 Jul 2023, 08:07
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JAAX7
If r and s are positive integers, is r/s a terminating decimal?

(1) r is a factor of 100
(2) s is a factor of 500
Statement 1:
100= 2^2 X5^2
Since r is a factor of 100, r could be anything. r= 2,5,4,20,25,50,100
No clear information about s . so cancel A and D
Statement 2:
500= 2^2 X5^3
Since s is a factor of 500, s could be anything. s= 2,5,4,20,25,50,100,125,250,500
No clear information about r . so cancel B
Statement 1+2:
r s r/s
2 2 2/2=1 not a terminating decimal
5 2 5/2=2.5 terminating decimal
2 5 2/5=0.4 terminating decimal

Multiple answers, so cancel C
Option E is correct
Show more

---+---

What is a terminating decimal?

Is 1 or any other whole number can't be expressed in decimal format (such as 1 is equivalent to 1.0)? If yes, shall this also be considered as a terminating decimal?If true, then correct answer choice should be 'B'.

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If r and s are positive integers, is r/s a terminating decimal? 03 Jul 2023, 11:48
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ssinghal087
JAAX7
If r and s are positive integers, is r/s a terminating decimal?

(1) r is a factor of 100
(2) s is a factor of 500
Statement 1:
100= 2^2 X5^2
Since r is a factor of 100, r could be anything. r= 2,5,4,20,25,50,100
No clear information about s . so cancel A and D
Statement 2:
500= 2^2 X5^3
Since s is a factor of 500, s could be anything. s= 2,5,4,20,25,50,100,125,250,500
No clear information about r . so cancel B
Statement 1+2:
r s r/s
2 2 2/2=1 not a terminating decimal
5 2 5/2=2.5 terminating decimal
2 5 2/5=0.4 terminating decimal

Multiple answers, so cancel C
Option E is correct

---+---

What is a terminating decimal?

Is 1 or any other whole number can't be expressed in decimal format (such as 1 is equivalent to 1.0)? If yes, shall this also be considered as a terminating decimal?If true, then correct answer choice should be 'B'.

Posted from my mobile device
Show more

A terminating decimal is a decimal number that ends or terminates after a finite number of digits, meaning there are no repeating digits or an infinite sequence of digits after the decimal point. For example, 0.75, 2.5, 7 (an integer IS a decimal with a finite number of nonzero digits) and 7.125 are all terminating decimals. A non-terminating decimal is a decimal number that does not end or terminate after a finite number of digits, meaning it goes on infinitely. For example, 0.6666... is a non-terminating decimal because the digit 6 repeats infinitely or decimal expansion of pi is 3.14159265358979323846... is non-terminating because it goes on infinitely.

A terminating decimal is obtained when a fraction, reduced to its lowest term, has no prime factors other than 2 and/or 5 in the denominator. In other words, if a fraction is simplified and has only the prime factors of 2 and/or 5 in the denominator, then the resulting decimal will terminate. For example, 1/4 and 7/20 are both fractions that have no prime factors other than 2 and/or 5 in the denominator, and so their decimal representations terminate (0.25 and 0.35, respectively).

Conversely, a non-terminating decimal is obtained when a fraction, reduced to its lowest term, has prime factors other than 2 and/or 5 in the denominator. In other words, if a fraction is simplified and has prime factors other than 2 and/or 5 in the denominator, then the resulting decimal will be non-terminating. For example, the fraction 1/3, when expressed as a decimal, is non-terminating and repeating (0.333...), because 3 is a prime factor that is not 2 or 5.

In summary, whether a decimal terminates or not depends on the prime factors of the denominator when the fraction is reduced to its lowest term. If the denominator has only prime factors of 2 and/or 5, then the decimal representation will terminate. Otherwise, it will be non-terminating.

Now, back to the original question, the correct choice indeed is B. This is because 500 = 2^2*5^3 and thus any factor of 500 will exclusively have the prime factors of 2 and/or 5 in the denominator, which results in r/s being a terminating decimal.

Hope it helps.
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