How do you change the repeating decimal .3333333 into a percent?

Answer 1

Step 1:

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

Step 2:

Examine the repeating decimal to find the repeating digit(s)

Step 3:

Place the repeating digit(s) to the left of the decimal point

Step 4:

Place the repeating digit(s) to the right of the decimal point

Step 5:

Subtract the left sides of the two equations.Then, subtract the right sides of the two equations

As you subtract, just make sure that the difference is positive for both sides

Now let's practice converting repeating decimals to fractions with two good examples

Example #1:

What rational number or fraction is equal to 0.55555555555

Step 1:

x = 0.5555555555

Step 2:

After examination, the repeating digit is 5

Step 3:

To place the repeating digit ( 5 ) to the left of the decimal point, you need to move the decimal point 1 place to the right

Technically, moving a decimal point one place to the right is done by multiplying the decimal number by 10.

When you multiply one side by a number, you have to multiply the other side by the same number to keep the equation balanced

Thus, 10x = 5.555555555

Step 4:

Place the repeating digit(s) to the right of the decimal point

Look at the equation in step 1 again. In this example, the repeating digit is already to the right, so there is nothing else to do.

x = 0.5555555555

Step 5:

Your two equations are:

10x = 5.555555555

x = 0.5555555555

10x - x = 5.555555555 − 0.555555555555

9x = 5

Divide both sides by 9

x = 5/9

So... .3333 (repeating) is 3/9