Question

state wheather following rational numbers have terminating decimal expansion or not. If it has terminating decimal expansion. find it .​

Answer 1

Answer:

1) non terminating

2) terminating = 0.009375

3) non terminating

4) terminating = 0.00416

5) terminating = 2.125

6) terminating = 0.7

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Answer 2

Answer:

Theorem: Let x= p/q

be a rational number, such that the prime factorisation of q is of the form 2^n × 5^m , where n, m are non-negative integers. Then, x has a decimal expansion which terminates.

i) 29/343

Factorise the denominator, we get

343=7×7×7=7^3

So, denominator is not in form of 2^n×5^m

so, 29/343 is not terminating

ii) 15/1600

Factorise the denominator, we get

1600=2×2×2×2×2×2×5×5= 2^6 × 5^2

So, denominator is in form of 2^n×5^m

so, 15/1600 is terminating.

iii) 77/210

Divide numerator and denominator both by 7 we get 11/30

Factorise the denominator, we get

30 = 2×3×5

So, denominator is not in the form of 2^n×5^m

so, 77/210 is not terminating.

iv) 13/3125

Factorise the denominator, we get

3125=5×5×5×5×5=5^5

So, denominator is in form of 5^m. So, 13/3125 is terminating.

v) 17/8

Factorise the denominator, we get

8=2×2×2=2^3

So, denominator is in form of 2^n.

so, 17/8 is terminating.

vi) 35/50

Divide numerator and denominator both by 5 we get 7/10

Factorise the denominator, we get

10=2×5

So, denominator is in form of 2^n×5^m.

so, 35/50 is terminating.