Question

Describe how to write a decimal with 12 repeating digits as a fraction.

Answer 1

Answer: Here are the basic steps as to write any decimal with any amount of repeating digits as a fraction!

1. Create an equation such that x equals the decimal number.

2. Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10y.

3. Subtract the second equation from the first equation.

4. Solve for x.

5. Reduce the fraction.

Let's use the repeating decimal 0.6... with the digit 6 repeating as our example.

Hint: The six's in bold are repeating.

x = 0.6

10x = 6.6

10x - x = 6.6 - 0.6

9x = 6

x = 6/9 or 2/3