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6.02 Comparing and ordering fractions, decimals, and percents

Lesson

Now that we know how to convert both fractions and decimals into percentages, it's time to play around with them a bit and compare these different types of numbers.

Remember!

The greater than symbol is written as $>$> and will have the larger number on the left, for example, $5>2$5>2

The less than symbol is written as $<$< and will have the larger number on the right, for example, $2<5$2<5

Ascending order means smallest to largest, for example, $-2,3,5,8$2,3,5,8

Descending order means largest to smallest, for example, $10,5,2,-1$10,5,2,1

 

Worked example

Question 1

Compare the numbers $0.7$0.7, $25%$25% and $\frac{1}{3}$13 and put them in ascending order

Think: How can I put them all in the same form so I can compare them easily?

Do: Let's convert both $0.7$0.7 and $\frac{1}{3}$13 into percentages.

$0.7\times100$0.7×100 $=$= $70$70
$0.7$0.7 $=$= $70%$70%
     
$\frac{1}{3}$13 $=$= $33\frac{1}{3}$3313 $%$%

So: $25%$25% < $33\frac{1}{3}$3313% < $70%$70%

Therefore the ascending order is: $25%$25%, $\frac{1}{3}$13, $0.7$0.7

Practice questions

QUESTION 2

Arrange $\frac{9}{10}$910, $40%$40% and $0.5$0.5 in descending order.

  1. First, convert $\frac{9}{10}$910 to a percentage.

  2. Now convert $0.5$0.5 to a percentage.

  3. Which of the following arranges $\frac{9}{10}$910, $40%$40% and $0.5$0.5 from largest to smallest?

    $40%$40%, $\frac{9}{10}$910, $0.5$0.5

    A

    $\frac{9}{10}$910, $0.5$0.5, $40%$40%

    B

    $\frac{9}{10}$910, $40%$40%, $0.5$0.5

    C

    $0.5$0.5, $40%$40%, $\frac{9}{10}$910

    D

    $40%$40%, $\frac{9}{10}$910, $0.5$0.5

    A

    $\frac{9}{10}$910, $0.5$0.5, $40%$40%

    B

    $\frac{9}{10}$910, $40%$40%, $0.5$0.5

    C

    $0.5$0.5, $40%$40%, $\frac{9}{10}$910

    D

QUESTION 3

Consider the values $71%$71% and $0.31$0.31.

  1. First convert $0.31$0.31 to a percentage.

  2. Select the inequality sign that makes the statement true.

    $71%$71% ? $0.31$0.31

    $=$=

    A

    $>$>

    B

    $<$<

    C

    $=$=

    A

    $>$>

    B

    $<$<

    C

QUESTION 4

Consider the statement:

$\frac{67}{50}$6750 > $154%$154%

  1. First convert $\frac{67}{50}$6750 to a percentage

  2. Hence, is the statement True or False?

    True

    A

    False

    B

    True

    A

    False

    B

QUESTION 5

Consider the following values:

$71%$71%, $\frac{4}{6}$46, $\frac{84}{1000}$841000, $0.7$0.7, $0.99$0.99, $50.8%$50.8%

  1. Which has the largest value?

    $71%$71%

    A

    $\frac{84}{1000}$841000

    B

    $\frac{4}{6}$46

    C

    $50.8%$50.8%

    D

    $0.7$0.7

    E

    $0.99$0.99

    F

    $71%$71%

    A

    $\frac{84}{1000}$841000

    B

    $\frac{4}{6}$46

    C

    $50.8%$50.8%

    D

    $0.7$0.7

    E

    $0.99$0.99

    F
  2. Which has the smallest value?

    $\frac{84}{1000}$841000

    A

    $50.8%$50.8%

    B

    $0.99$0.99

    C

    $71%$71%

    D

    $0.7$0.7

    E

    $\frac{4}{6}$46

    F

    $\frac{84}{1000}$841000

    A

    $50.8%$50.8%

    B

    $0.99$0.99

    C

    $71%$71%

    D

    $0.7$0.7

    E

    $\frac{4}{6}$46

    F
  3. Which has a value closest to $0.5$0.5?

    $0.99$0.99

    A

    $\frac{4}{6}$46

    B

    $50.8%$50.8%

    C

    $0.7$0.7

    D

    $71%$71%

    E

    $\frac{84}{1000}$841000

    F

    $0.99$0.99

    A

    $\frac{4}{6}$46

    B

    $50.8%$50.8%

    C

    $0.7$0.7

    D

    $71%$71%

    E

    $\frac{84}{1000}$841000

    F

Outcomes

7.RP.3

Use proportional relationships to solve multistep ratio and percent problems.

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