Covert the rational into decimals without actual divisin
Answers
Answer:
Answer:To find out we have terminating decimals in fractions, we observe prime factors of the denominators.
So,
if we have only 2 and 5 (if only 2 or even only 5 also) as the prime factors of the denominator of a rational number in the lowest form, the given fractional number will have terminating decimal representation.
Here, If we see all numbers,
so
we may note that all the above given numbers (except ) are in the lowest form.
(i) The denominator of is 128.
Now,
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
The prime factor of 128 is 2 seven times.
Therefore, has a terminating decimal representation.
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(ii) The denominator of is 125.
Now,
125 = 5 × 5 × 5
The prime factor of 125 is 5 three times.
Therefore, has a terminating decimal representation.
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(iii) The denominator of is 24.
Now,
24 = 2 × 2 × 2 × 3
The prime factor of 24 are 2 and 3. One of the factors is other than 2 and 5. But the rational number is not in the lowest form.
In fact , whose denominator 8 = 2 × 2 × 2.
Therefore, has a terminating decimal representation.
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(iv) The denominator of is 90.
Now,
90 = 2 × 3 × 3 × 5
The prime factor of 90 are 2, 3, 5.
One of the factors is other than 2 and 5.
Therefore, will not have a terminating decimal representation.