Massachusetts 7 - 2020 Edition
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 multi-step ratio, rate, and percent problems. Examples: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.