Question

which of the following numbers is a terminating decimala) v12 b) 7/8 c) 5/11 d) 0.81818181...(That v i put is just the square root symbol)

Answer 1

Given: The numbers are provided.

To find: Which is a terminating decimal.

Step-by-step explanation:

Terminating decimal: A terminating decimal has finite number of digits after the decimal point.

It must be a rational number.

It must not have a bar over the finite digits occuring after the decimal point.

1)Let us check the first number

`√(12)`

the number is not a perfect square hence it is an irrational number therefore it is not a terminating decimal.

(for a number to be a terminating decimal it must be a rational number)

2)The next number is 7/8.

The number in decimal form can be expressed as 7/8=0.875

we can observe there are finite number of digits after decimal hence it is a terminating decimal.

3) The thirs number is 5/11

when expressed in decimal form we get

`\begin{gathered} (5)/(11)=0.454545... \\ =0.\bar{45} \end{gathered}`

we have repeating terms after decimal hence it is not a terminating decimal.

4)the fourth number 0.81818181...

this can be expressed as

`0.\bar{81}`

in this also we have repeating terms after decimal the term 81 is repeating.

hence, it is not a terminating decimal.

Final Answer: The number 7/8 is a terminating decimal. Option (b)