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

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