6.02 Comparing and ordering fractions, decimals, and percents
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.
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
AFalse
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
FWhich 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
FWhich 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