without actual division find which of the following rational are terminating decimal 13 by 80
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without actual division find which of the following rational are terminating decimal 13 by 80
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Answer:
We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressible as a terminating, otherwise it has non - terminating repeating decimal representation. Thus, we will have to check the prime factors of the denominators of each of the given rational numbers.
In \frac{13}{80}
80
13
, the denominator is 80.
We have, 80 = 2 × 2 × 2 × 2 × 5.
Thus, 80 has only 2 and 5 as prime factors.