Question

Which of the following fractions is recurring decimal?
(1)237/625

(2)125/192

(3)1000/1024

(4)2008/2560

Answer 1

Answer:

If denominator of any rational number can be factorised in the for of 2^m5^n, then the decimal expansion is terminating otherwise non terminating.

now prime factors of 192 = 2^6 x3

so 125/192 is non terminating.

1000/1024 = 250/512 = 125/256

prime factors of 256 = 2^8

so its decimal expansion is terminating.

2008/2560 = 502/640 = 251/320

prime factors of 320 = 2^6 × 5

so its decimal expansion is terminating.

Answer 2

you can know how the following fractions are the curing decimals by dividing it and if the answer after the decimal two or three numbers are repeating again and again and it will be a recurring decimal like ok we can take the example of second one divide 125 by 192 and the answer will be 0.6510416667so this is a recurring decimal where the no. 6 is coming again and again so we round of 6 and and it will become 7 so the repeating 6 will stop