Comparing Decimals and Fractions

Learning Outcomes

Order decimals and fractions

Order Decimals and Fractions

In an 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 $({\Large\frac{3}{8}})$ and $(0.4)$ using $<$ or $\text{>.}$

Solution

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

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

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Solution

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

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example

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

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Solution

	${\Large\frac{13}{20}},0.61,{\Large\frac{11}{16}}$
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.	$0.61,{\Large\frac{13}{20}},{\Large\frac{11}{16}}$

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To see more examples, watch this video example.

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Unit 1

Learning Outcomes

Order Decimals and Fractions

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