Question

5. Without actual division, find which of the following rational numbers have terminating decimal expansion.

(i) 7/128 (ii) 21/15 (iii

Answer 1

Answer:

Step-by-step explanation:

Given  

5. Without actual division, find which of the following rational numbers have terminating decimal expansion. (i) 7/128 (ii) 21/15

We know that to find p/q is terminating we have

1. P and q are co-prime and

2. Q is of the form 2^n 5^m where n and m are non-negative integers.

1. Checking co-prime.

7 and 128 have no common factors, so 7 and 128 are co-prime.

For denominator, factors are

128 = 2^7

      = 2^7 x 5^0

      = 2^n 5^m

So n = 7 and m = 0

So 7/128 is a terminating decimal.

We know that to find p/q is terminating we have

3. P and q are co-prime and

4. Q is of the form 2^n5^m where n and m are non-negative integers.

2. Checking co-prime. Taking 21/15 = 7/5

7 and 5 have no common factors, so 7 and 5 are co-prime.

For denominator, factors are

5 = 5^1

      = 1 x 5

      = 2^0 x 5^1

      = 2^n 5^m

So n = 0 and m = 5

So 7/5 is a terminating decimal