Question

check whether it is terminating or non terminating

a) 23/9
b) 3/100
c) 1/5
d) 22/7

pls help me pls friends​

Answer 1

Answer:

a) non terminating

b)terminating

c)terminating

d)non terminating

Answer 2

Concept used:

If the denominator of the number can be represented in the form of 2ᵐ × 5ⁿ, then the given fraction would have a terminating decimal expansion.

Else, the fraction would have a non-terminating decimal expansion.

For example,

$\sf{\dfrac{57}{100}=\dfrac{57}{2^{2}\times5^{2}}}$

So, 3/100 has a terminating decimal expansion.

Let's solve the given question:

a) 23/9

Since 9 cannot be represented in the form 2ᵐ × 5ⁿ, This fraction has a non-terminating decimal expansion.

b) 3/100

100 can be represented as 2² × 5². So, it has a terminating decimal expansion.

c) 1/5

5 can be represented as 2⁰ × 5¹. So, it has a terminating decimal expansion.

d) 22/7

7 cannot be represented as 2ᵐ × 5ⁿ. So, it has a non-terminating decimal expansion.

KNOW MORE:

Terminating decimal expansion means the decimal expansion of the fraction has an end when we are dividing it by long division.