^

# How to convert fractions to decimals - beginner lesson

Some fractions are easy to write as decimals, because their denominator is a power of ten (10, 100, 1000, etc.), or because you can find an equivalent fraction with a denominator that is a power of ten. For example, 3/4 = 75/100, and then you just write 75/100 as 0.75. Or, 3/8 = 375/1000 = 0.375.

But most of the time we need to use division to change a fraction into a decimal. This means either long division or dividing with a calculator.

For example, to convert 5/13 into a decimal, you divide 5 by 13. In long division, you might add decimal zeros to the dividend (5) before you even start, for example so it becomes 5.00000.

Often, these divisions don't terminate, but we do notice a PATTERN in the decimal digits — and also in the remainders that show up in long division.

In fact, any fraction (rational number), when written as a decimal, either has a repeating pattern in the digits that goes on forever, or the decimal terminates.

And... irrational numbers are such that cannot be written as fractions, and their decimal representation does NOT contain any repeating pattern in the digits.