Question

Without actually performing the long division state 129/500 will have a terminating decimals or non terminating repeating decimals expansion

Answer 1

Answer:

it is terminating decimals

Step-by-step explanation:

1. lcm of 500
2. 129/2×2×5×5×5

• so it is from of 2m 5n will have terminating decimal

Answer 2

Answer:

The answer is - the number has terminating decimal expansion

Step-by-step explanation:

To find number $\frac{129}{500}$ will have a terminating or non-terminating but repeating(recurring) decimal expansion without actually doing long division

Step = Observe the denominator

We know that if the L.C.M of denominator of the fraction has factors - 2 or power of 2/5 or power of 5/both then it will always have terminating decimal expansion if not then non-terminating but repeating[recurring] decimal expansion

That is

Denominator of the number $\frac{129}{500}$ is 500

500 = 5 X 100 = $5^{2}$ X 20 =  

The number $\frac{129}{500}$ has terminating decimal expansion because its denominator has power of 5 and also power of 2(i.e. $5^{3}$ X  $2^{2}$)