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.

First, convert $\frac{9}{10}$910 to a percentage.
Now convert $0.5$0.5 to a percentage.
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

QUESTION 3

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

First convert $0.31$0.31 to a percentage.
Select the inequality sign that makes the statement true.

$71%$71% ? $0.31$0.31

$=$=
A
$>$>
B
$<$<
C

QUESTION 4

Consider the statement:

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

First convert $\frac{67}{50}$6750 to a percentage
Hence, is the statement True or False?
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%

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
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
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

Outcomes

6.NS.7

Understand ordering and absolute value of rational numbers.

6.NS.7.a

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

2.11 Compare and order fractions, decimals, percents