LESSON: Fractions and Decimals

Decimals and Fractions

READ: Write Decimals as Fractions

Write Decimals as Fractions

Now that we have mastered writing fractions as decimals, it will be good to know how to go back the other way and write decimals as fractions.

Consider again the decimal 0.1. We already know that we can say that this number is “one-tenth.” It’s very easy to rewrite decimals as fractions because decimals are already expressed as fractions with a denominator that is a factor of ten.

0.1 = \frac{1}{10}, 0.01 = \frac{1}{100}

We can also say that 0.86 = \frac{86}{100}.

To convert decimals to fractions, we write the number to the right of the decimal place over a denominator equivalent to the last place value of the decimal number. So, if we have 0.877, we would write \frac{877}{1000}.

If we have simply 0.6, we can write \frac{6}{10}, or in simplest terms, \frac{3}{5}. Always make sure to put your fraction in simplest terms.


Example 1

Convert 0.35 to a fraction.

Start by saying the decimal to yourself out loud. To say 0.35 out loud, we can say “35 hundredths,” so we can go ahead and write the fraction down.

\frac{35}{100}

That’s a big fraction. We want to make our lives a little bit easier, so we will reduce the fraction to simplest terms. This fraction expressed in simplest terms is \frac{7}{20}.

Our final answer is \frac{7}{20}.


Example 2

Convert 2.4 to a mixed number.

Just as we leave aside the whole number when converting mixed numbers to decimals, we will leave aside the numbers to the left of the decimal point when converting decimals to fractions. So, in this case, we just have to find out what 0.4 is expressed as a fraction.

Let’s write it directly as the fraction “four tenths” or \frac{4}{10}. Can we simplify it? You bet. \frac{4}{10}=\frac{2}{5}.

2.4 expressed as a mixed number = 2 \frac{2}{5}.