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

##### 2 Answers

In mathematical exactitude, the value presentation is

#### Explanation:

In mathematical exactitude, the value presentation is

I have written this from the general formula

question, earlier. See

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.

#### 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"#