Question

without finding the decimal representation state whether the following rational number terminating decimal or non-terminating decimal
-5/10​

Answer 1

Answer:

Terminating decimal.

As 10 = 2 × 5, Factors of 10 only include 2 and 5, so it has a terminating decimal representation.

Explanation:

If the denominator of a number is divisible by factors of 10, 100, 1000 or so on.., then the decimal representation of the number is terminating.

Or we can say : if the denominator of a number has its factor only as powers of 2 and 5, then the decimal representation of the number is terminating.

Why this works?

let's choose any random number : 4, we know if we divide it by 10, then we will get a terminating value as we could just replace the decimal a little

4/10 = 0.4,

5.5/10 = 0.55

4.78/10 = 0.478

The same thing goes for any number of the form 10ⁿ, where n is an integer.

We can see

10 = 2 × 5

100 = 10 × 2 × 5

and so on.....

We can see the factors of 10 and 100 only includes powers of 2 and 5. So any number which has its denominator of the form 2ⁿ×5ᵃ has a terminating decimal representation.

Answer 2

without finding the decimal representation state whether the following rational number terminating decimal or non-terminating decimal

-5/10