# Benchmark Percentages & Decimals

Lesson

We know that whole numbers like $514$514 mean a number with $5$5 hundreds, $1$1 ten and $4$4 ones. Can you see that the units get smaller and and smaller as we go towards the right? But what does a decimal such as $0.45$0.45 mean? Well guess what, we can think of decimals in the same way so $0.45$0.45 can be thought of a number with $4$4 tenths and $5$5 hundredths. Check the diagram below if you're confused!

Well what does this mean when we want to switch between decimals and percentages? Let's see how It actually makes things a lot easier!

## From Decimals to Percentages

Let's take $0.4$0.4 for example. This means we have $0$0 ones and $4$4 tenths. In maths terms that means $4\times\frac{1}{10}$4×110 which equals $\frac{4}{10}$410, and we know this fraction can be converted to $40%$40%!

What about something like $0.75$0.75? Well, we can use the same steps. This number means $7\times\frac{1}{10}+5\times\frac{1}{100}$7×110+5×1100 which becomes $\frac{75}{100}$75100 and that is $75%$75%.

So what can we see so far from these kind of problems? Well what we've done is actually moved the decimal point two places to the right and transformed it into a percentage in both cases. This is because we have actually multiplied the decimal by $100%$100%. Try and multiple $0.4$0.4 and $0.75$0.75 by $100%$100% in your calculator and see what you get!

## From percentages to decimals

Going back from percentages to decimals is quite simple if we work backwards, we just divide by $100%$100%! Let's say we have $30%$30%, so $30%\div100%$30%÷​100% is $0.3$0.3, which is the same as shifting the imaginary decimal point to the right of the $0$0 left twice. To look at this another way, $30%$30% is $\frac{30}{100}=\frac{3}{10}$30100=310 as a fraction, which can be described as $3$3 tenths. This also describes the decimal $0.3$0.3.

With percentages like $25%$25% we can just take the number and put it after the decimal point as $0.25$0.25. Can you see this is just going in reverse of how we dealt with decimals like $0.75$0.75 above?

#### Example

##### Question 1

Express $0.6$0.6 as a percentage

Think of where the decimal place will be

Do: $0.6\times100%=60%$0.6×100%=60% (we moved the decimal point two places to the right)

##### Question 2

Calculate $85%$85% as a decimal

Think again of how to move the decimal place, especially after looking at the previous example

Do: $85%\div100%=85\div100$85%÷​100%=85÷​100 = $0.85$0.85 (moved the decimal point two places to the left)

##### QUESTION 3

A bushfire moves through an area of land, burning $20%$20% of the land.

1. Express how much of the land is burnt as a decimal to one decimal place.

2. Express how much of the land is not burnt as a decimal to one decimal place.

### 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.