LESSON: Fractions and Decimals

READ: Write Fractions as Terminating Decimals

Write Fractions and Mixed Numbers as Terminating Decimals

Now that you have mastered fractions and their corresponding operations, it’s time to discover how they relate to decimals. You know that fractions and decimals are related because they are both ways of describing numbers that are not wholes. In essence, a fraction is simply another way of describing what a decimal describes. They both represents parts of a whole and both can show the same part in a different way. The fraction shows us the part using the fraction bar comparing part to whole and the decimal shows us the part using place value. To start off, we’ll see how fractions can be converted into decimals and how decimals can be converted into fractions.

How do we convert fractions to decimals and decimals to fractions?

First, remember that fractions and decimals are different ways of writing the same thing. Both show us how to represent a part of a whole. Think about how we talk about fractions and decimals because this will become useful as we convert them.

Say this value out loud 0.1. You can say “point one” or you can say “one tenth.” Does the second version sound a little bit familiar? It sounds like the fraction $\frac{1}{10}$ . It turns out that $0.1 = \frac{1}{10}$ .

How do we convert fractions into decimals?

We can easily convert fractions into decimals. You’ve probably noticed by now that a fraction is really a short way of writing a division expression. Writing $\frac{3}{4}$ is really like writing $3 \div 4$ . The way that we find out how to write $\frac{3}{4}$ as a decimal is to go ahead and solve the division problem. Since 4 doesn’t go into 3, we have to expand the number over the decimal point.

${4 \overline{) {3.0 \;}}}$

How many times does 4 go into 3.0? Four goes into 3.0 .7 times.

$& \overset{ \ \ \ \ .7}{4 \overline{ ) {3.0 \;}}}\\ & \underline{-2.8 \ }\\ & \quad \ .2$

Be sure when you are writing your quotient above the dividend to keep the original place of the decimal point. Since 4 does not divide evenly into 3.0 and we have a remainder of .2, we can go further to the other side of the decimal point by adding a 0 next to the remainder of .2.

$& \overset{ \ \ \ \ .75}{4 \overline{ ) {3.00 \;}}}\\ & \ \underline{ \ -2.8 \ }\\ & \quad \ \ .20\\ & \ \underline{ \ \ -.20 \ }\\ & \quad \ \ \ \ \ 0$

4 goes evenly into .20 five times, so we have our final answer.

$\frac{3}{4} = 0.75$

Example 1

Convert $\frac{1}{4}$ to a decimal.

We start this by changing it into a division problem. We will be dividing 1 by 4. You already know that 1 can’t be divided by four, so you will need to use a decimal point and add zeros as needed.

$& \overset{ \ \ \ \ .25}{4 \overline{ ) {1.00 \;}}}\\ & \underline{-8 \quad \ }\\ & \quad \ 20\\ & \ \ \underline{-20 \ }\\ & \qquad 0$

Our answer is .25.

How do we convert mixed numbers to decimals?

When you are working with mixed numbers like $1 \frac{3}{4}$ for example, it is easiest to simply set the whole number to the side and solve the division problem with the fraction. When you have completed the division problem with the fraction, make sure that you put the whole number back on the left side of the decimal point.

$1 \frac{3}{4} = 1.75$

Example 2

Convert $3 \frac{1}{2}$ to a decimal.

First, set aside the 3. We will come back to that later.

Next, we divide 1 by 2. Use a decimal point and zeros as needed.

$& \overset{ \ \ \ \ .5}{2 \overline{ ) {1.0 \;}}}\\ & \underline{ \ -10}\\ & \quad \ 0$

Now we add in the 3.

Our final answer is 3.5.