Percentages

NZ Level 4

Comparing Decimals, Fractions and Percentages

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.

Let's take a look at the following question:

**Compare **the numbers $0.53$0.53, $60.3%$60.3%, and $\frac{17}{77}$1777 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 $0.53$0.53 and $\frac{17}{77}$1777 into percentages.

$0.53\times100$0.53×100 | $=$= | $53$53 |

$0.53$0.53 | $=$= | $53%$53% |

$\frac{17}{77}$1777 | $=$= | $\frac{17}{77}\times100$1777×100 $%$% |

$=$= | $\frac{1700%}{77}$1700%77 | |

$=$= | $22\frac{6}{77}$22677 $%$% |

$22\frac{6}{77}$22677% < $53%$53% < $60.3%$60.3%

Therefore the ascending order is: $\frac{17}{77}$1777, $0.53$0.53, $60.3%$60.3%

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$=$=

A$>$>

B$<$<

C

Compare: $0.31$0.31 and $45%$45%

First convert $0.31$0.31 to a percentage.

Which of the two values is greater?

$45%$45%

A$0.31$0.31

B$45%$45%

A$0.31$0.31

B

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

Know the equivalent decimal and percentage forms for everyday fractions