Question

Find an equivalent fraction for the repeating decimal: .

Answer 1

Step 1)

Let x  equal the repeating decimal you are trying to convert to a fraction

Step 2)

After examination, the repeating digit is 605

Step 3)

To place the repeating digit (605 ) to the left of the decimal point, we need to move the decimal point 3 places to the right.

moving a decimal point 3 places to the right is done by multiplying the decimal number by 1000.

Thus

Step-4)

Place the repeating digits to the right of the decimal point.

Step-5) The two equations are

Equivalent fraction is .

Answer 2

The repeating decimal is .

Let N be the represent the number,

Multiply each side by 1000 because three digit repeats.

Subtract N from 10N to eliminate the repeating part.

Resultant equation is .

Divide each side by 999.

The equivalent fraction of