Question

How do you write the repeating decimal 0.175 where 175 is repeated as a fraction?

Answer 1

In mathematical exactitude, the value presentation is

`10^(-3)1/(1-10^(-3))175`

Explanation:

In mathematical exactitude, the value presentation is

`10^(-3)1/(1-10^(-3))175`

I have written this from the general formula

`V = v + 10^(-m)/(1-10^(-n))P` given in my answer to a similar

question, earlier. See

socratic.org/questions/a-fraction-v-in-decimal-form-is-an-infinite-string-that-comprises-the-non-repeat?source=search

Here, V = value, v= value prefixing the repeating digits string, 10^(-m)

is the place value of the least significant digit (lsd ) in the

repeatend (reptend) in the infinitely-long string and n is the

number of digits in the reptend string P ( called Period )..

In this problem, v=0, m=3, n=3 and P=175.

Answer 2

`175/999`

Explanation:

We require to establish 2 equations with the same repeating fraction and subtract them to eliminate the repeating fraction.

Let `x=0.bar(175).......... (A)`

The bar above the digits 175 denotes 175 is repeated.

To obtain the same repeating fraction after the decimal point, we require to multiply (A) by 1000.

`rArr1000x=175.bar(175).......... (B)`

Now subtract (A) from (B)

`rArr999x=175`

`rArrx=175/999larr" in simplest form"`