Question

1. The decimal form of 129/22 5272 is (a) terminating (b) non-termining (c) non-terminating non-repeating (d) none of the above​

Answer 1

Answer:

Given rational number is

2

2

×5

7

×7

5

129

.

We know,

q

p

is terminating if:

a) p and q are co-prime and

b) q is of the form of 2

n

×5

m

, where n and m are non-negative integers.

Firstly, we check whether the numerator and denominator are co-prime,

Numerator =129=3∗43

Denominator =2

2

×5

7

×7

5

⇒129 and 2

2

×5

7

×7

5

have no common factors.

Therefore, 129 and 2

2

×5

7

×7

5

are co-prime.

Now, we check whether q is in the form of 2

n

×5

m

,

Denominator =2

2

×5

7

×7

5

So, the denominator is not of the form 2

n

×5

m

.

Thus,

2

2

×5

7

×7

5

129

is a non-terminating repeating decimal.

Step-by-step explanation:

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