Ordering Decimals and Fractions
Ordering Decimals and Fractions
Earlier, 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 \(\frac{3}{8}\_\_0.4\) using \(<\) or \(\text{>.}\)
Solution
| \(\frac{3}{8}\_\_0.4\) | |
| Convert \(\frac{3}{8}\) to a decimal. | \(0.375\_\_0.4\) |
| Compare \(0.375\) to \(0.4\) | \(0.375<0.4\) |
| Rewrite with the original fraction. | \(\frac{3}{8}<0.4\) |
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 \(-0.5\_\_\_-\frac{3}{4}\) using \(<\) or \(\text{>.}\)
Solution
| \(-0.5\_\_\_-\frac{3}{4}\) | |
| Convert \(-\frac{3}{4}\) to a decimal. | \(-0.5\_\_\_-0.75\) |
| Compare \(-0.5\) to \(-0.75\). | \(-0.5>-0.75\) |
| Rewrite the inequality with the original fraction. | \(-0.5>-\frac{3}{4}\) |
Example
Write the numbers \(\frac{13}{20},0.61,\frac{11}{16}\) in order from smallest to largest.
Solution
| \(\frac{13}{20},0.61,\frac{11}{16}\) | |
| Convert the fractions to decimals. | \(0.65,0.61,0.6875\) |
| Write the smallest decimal number first. | \(0.61,\_\_\__,\_\_\_\_\_\) |
| Write the next larger decimal number in the middle place. | \(0.61,0.65,\_\_\_\_\_\) |
| Write the last decimal number (the larger) in the third place. | \(0.61,0.65,0.6875\) |
| Rewrite the list with the original fractions. | \(0.61,\frac{13}{20},\frac{11}{16}\) |
Optional Video: Compare Fractions and Decimals using Inequality Symbols
This lesson is part of:
Introducing Decimals
View Full Tutorial