Question

how you would convert the repeating, nonterminating decimal to a fraction? Please EXPLAIN the process as you solve the problem, 0.1515... I need answers in words and numbers, I need and explanation for each numerical step

Answer 1

Hey there!!

The decimal given - 0.15151515

Let's take this given decimal as ' x '

As the periodicity is 2 we multiply x and the number by 100.

What is periodicity?

Ans - Periodicity is the number of digits repeating.

In the given decimal, the number repeating is 15, and the number of digits is equal to 2 and hence periodicity is 2.

If the periodicity is 1, then we multiply by 10 and if it is 3 , then we multiply with 1000 and continues.

We have got :

x = 0.1515151515

100 ( x ) = 100 ( 0.151515151515 )

... 100x = 15.151515

The two equations we got :

100x = 15.1515 ------- ( 1 )

x = 0.1515 --------- ( 2 )

Now, let's subtract the second equation from the first.

We get ,

... 99x = 15

Divide 99 on both sides

... x = 15 / 99

At the start we knew x = 0.151515

Now plug in the value

0.151515 = 15 / 99

Hence, the fractional or the rational form of 0.151515 is 15/99

Simplified answer - 5 / 33

Hope my answer helps!!

Answer 2

Let x = 0.151515.... (1)

Notice the number of integers that are repeating. Here 1 and 5 are repeating.

So, multiply both sides of the above expression by 100. (If only one integer is repeating, you need to multiply by 10, if 3 integers repeating, you need to multiply by 1000 and so on.)

So, (1) becomes,

100x = 15.151515.... (2)

(2) - (1) gives,

99x = (15.151515.....) - (0.151515....)

= 15

`x=(15)/(99)`