 # Benchmark Percentages comparing with Decimals and Fractions

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:

##### 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

##### 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

### Outcomes

#### NA3-1

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.

#### NA3-5

Know fractions and percentages in everyday use.