# 2.11 Compare and order fractions, decimals, 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

#### 6.NS.7

Understand ordering and absolute value of rational numbers

#### 6.NS.7a

a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.