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Study Guides > Prealgebra

Comparing Decimals and Fractions

Learning Outcomes

  • Order fractions and decimals by writing fractions as decimals
 

Order Decimals and Fractions

In Decimals, 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](\frac{3}{8}) (0.4)[/latex] using [latex]<[/latex]; or [latex]\text{>.}[/latex] Solution
[latex](\frac{3}{8}) (0.4)[/latex]
Convert [latex]\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]\frac{3}{8}<0.4[/latex]
 

try it

[ohm_question]146286[/ohm_question]
  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) (-\frac{3}{4})[/latex] using [latex]<[/latex]; or [latex]\text{>.}[/latex]

Answer: Solution

[latex](-0.5) (-\frac{3}{4})[/latex]
Convert [latex]-\frac{3}{4}[/latex] to a decimal. [latex](-0.5) (- 0.75)[/latex]
Compare [latex]-0.5[/latex] to [latex]-0.75[/latex] . [latex]-0.5>-0.75[/latex]
Rewrite the inequality with the original fraction. [latex]-0.5>-\frac{3}{4}[/latex]

 

try it

[ohm_question]146290[/ohm_question]
 

example

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

Answer: Solution

[latex]\frac{13}{20},0.61,\frac{11}{16}[/latex]
Convert the fractions to decimals. [latex]0.65,0.61,0.6875[/latex]
Write the smallest decimal number first. [latex]0.61,____,_____[/latex]
Write the next larger decimal number in the middle place. [latex]0.61,0.65,_____[/latex]
Write the last decimal number (the larger) in the third place. [latex]0.61,0.65,0.6875[/latex]
Rewrite the list with the original fractions. [latex]0.61,\frac{13}{20},\frac{11}{16}[/latex]

 

try it

[ohm_question]146294[/ohm_question]
To see more examples, watch this video example. https://youtu.be/f4theaYuVuo

Licenses & Attributions

CC licensed content, Original

  • Question ID 146286, 146290, 146294. Authored by: Lumen Learning. License: CC BY: Attribution.

CC licensed content, Shared previously

  • Ex: Order Fractions and Decimals From Least to Greatest. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.

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