2. Rational numbers

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

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

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$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

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$=$=

A$>$>

B$<$<

C

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

BTrue

AFalse

B

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$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

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

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$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

Understand ordering and absolute value of rational numbers.

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