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 [latex]({\Large\frac{3}{8}}) (0.4)[/latex] using [latex]<[/latex]; or [latex]\text{>.}[/latex]

Solution

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

 

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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 [latex](-0.5) (-{\Large\frac{3}{4}})[/latex] using [latex]<[/latex]; or [latex]\text{>.}[/latex]

 

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example

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

 

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To see more examples, watch this video example.