Changing Infinite Repeating Decimals to Fractions

Remember: Infinite repeating decimals are usually represented by putting a line over (sometimes under) the shortest block of repeating decimals. Every infinite repeating decimal can be expressed as a fraction.

Find the fraction represented by the repeating decimal equation.

Let n stand for equation or 0.77777 …

So 10 n stands for equation or 7.77777 …

10 n and n have the same fractional part, so their difference is an integer.

equation

You can solve this problem as follows.

equation

So equation

Find the fraction represented by the repeating decimal equation.

Let n stand for equation or 0.363636 …

So 10 n stands for equation or 3.63636 …

and 100 n stands for equation or 36.3636 …

100 n and n have the same fractional part, so their difference is an integer. (The repeating parts are the same, so they subtract out.)

equation

You can solve this equation as follows:

equation

Now simplify equation to equation.

So equation

Find the fraction represented by the repeating decimal equation.

Let n stand for equation or 0.544444 …

So 10 n stands for equation or 5.444444 …

and 100 n stands for equation or 54.4444 …

Since 100 n and 10 n have the same fractional part, their difference is an integer. (Again, notice how the repeated parts must align to subtract out.)

equation

You can solve this equation as follows.

equation

So equation