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Study Guides > Mathematics for the Liberal Arts Corequisite

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 (38)(0.4)({\Large\frac{3}{8}}) (0.4) using <<; or >.\text{>.} Solution
(38)(0.4)({\Large\frac{3}{8}}) (0.4)
Convert 38\Large\frac{3}{8} to a decimal. (0.375)(0.4)(0.375) (0.4)
Compare 0.3750.375 to 0.40.4 0.375<0.40.375<0.4
Rewrite with the original fraction. 38<0.4{\Large\frac{3}{8}}<0.4
 

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 (0.5)(34)(-0.5) (-{\Large\frac{3}{4}}) using <<; or >.\text{>.}

Answer: Solution

(0.5)(34)(-0.5) (-{\Large\frac{3}{4}})
Convert 34-{\Large\frac{3}{4}} to a decimal. (0.5)(0.75)(-0.5) (- 0.75)
Compare 0.5-0.5 to 0.75-0.75 . 0.5>0.75-0.5>-0.75
Rewrite the inequality with the original fraction. 0.5>34-0.5>-{\Large\frac{3}{4}}

 

try it

[ohm_question]146290[/ohm_question]
 

example

Write the numbers 1320,0.61,1116{\Large\frac{13}{20}},0.61,{\Large\frac{11}{16}} in order from smallest to largest.

Answer: Solution

1320,0.61,1116{\Large\frac{13}{20}},0.61,{\Large\frac{11}{16}}
Convert the fractions to decimals. 0.65,0.61,0.68750.65,0.61,0.6875
Write the smallest decimal number first. 0.610.61 , _____ , _____
Write the next larger decimal number in the middle place. 0.61,0.650.61,0.65 , _____
Write the last decimal number (the larger) in the third place. 0.61,0.65,0.68750.61,0.65,0.6875
Rewrite the list with the original fractions. 0.61,1320,11160.61,{\Large\frac{13}{20}},{\Large\frac{11}{16}}

 

try it

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

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