## Comparing Decimals and Fractions

### Learning Outcomes

• Order fractions and decimals by writing fractions as decimals

## Order Decimals and Fractions

In and earlier lesson, we compared two decimals and determined which was larger. To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals.

### example

Order $({\Large\frac{3}{8}}) (0.4)$ using $<$; or $\text{>.}$

Solution

 $({\Large\frac{3}{8}}) (0.4)$ Convert $\Large\frac{3}{8}$ to a decimal. $(0.375) (0.4)$ Compare $0.375$ to $0.4$ $0.375<0.4$ Rewrite with the original fraction. ${\Large\frac{3}{8}}<0.4$

### try it

When ordering negative numbers, remember that larger numbers are to the right on the number line and any positive number is greater than any negative number.

### example

Order $(-0.5) (-{\Large\frac{3}{4}})$ using $<$; or $\text{>.}$

### example

Write the numbers ${\Large\frac{13}{20}},0.61,{\Large\frac{11}{16}}$ in order from smallest to largest.

### try it

To see more examples, watch this video example.