LESSON: Fractions and Decimals

READ: Compare and Order Decimals and Fractions

Compare and Order Decimals and Fractions

Eventually, you will be able to convert common fractions to decimals and common decimals to fractions in your head. You already know some of the classics like $0.5 = \frac{1}{2}$ . Knowing this off the top of your head will make it easy for you to compare and order between fractions and decimals. For now, we will use our expertise at converting to compare and order. It’s always helpful to check.

Example

Compare $\frac{1}{4}$ and 0.25 using <, > or =

To compare a fraction to a decimal or a decimal to a fraction, we will need to convert one of them, so that we can compare a fraction to a fraction or a decimal to a decimal. For this one, I will convert $\frac{1}{4}$ to a decimal. I divide 1.0 by 4. 4 goes into 1.0 .2 times. There is also a remainder of 0.20 and 4 goes into 0.20 0.05 times. Now we know that $\frac{1}{4}$ written as a decimal is 0.25.

We compare it as $\frac{1}{4} = 0.25$ .

Example

Compare $1 \frac{2}{20}$ and 1.30

Our work in estimating the value of fractions and rounding decimals can be helpful when comparing fractions and decimals because you can look at a fraction or a decimal and quickly have a sense of what the approximate value is. Take a look at the mixed number $1 \frac{2}{20}$ . Don’t be intimidated by the large denominator, it looks like we can simplify it. If we simplify it to $1 \frac{1}{10}$ .

Now we can take 1.30 and make it a mixed number. 1.30 becomes $1 \frac{3}{10}$ .

Our final answer is that $1 \frac{2}{20} < 1.30$ .

We can use all of these strategies when ordering fractions and decimals too. Be sure that they are in the same form and then order them from least to greatest or from greatest to least.