A percentage is a fraction with a denominator of 100. The only thing that is weird about percentages is the slightly peculiar notation.

The fraction $\frac{42}{100}$ can be written as $42\%$, but there is no conceptual difference between the two. Both of them are percentages.

1. $0.5$ is not a percentage, though as we will discover in the next example, it can be written as a percentage.
2. This is a percentage $\frac{40}{100}$ is $40\%$.
3. $50\%$ is a percentage.
4. $\frac{3}{10}$ is not a percentage, though it can, like any fraction, be converted to one.
5. Do not fall into the trap of thinking that you cannot have more than 100% of something. There are some things where you cannot have more than 100% of a thing, like the percentage of your effort in any circumstance, but there are many situations where you can have more than $100\%$.
6. Another percentage which is bigger than $100\%$

To convert a decimal number to a percentage, you must multiply by $100$. Nothing else. That is all!

When you have a simple fraction, which is easy to turn into an equivalent fraction over $100$, then that is the most straight forward method to use. This is the first method on the left.

It is also perfectly okay to turn the fraction into a decimal and then multiply by $100$ to turn it into a percentage. This is the second method on the left.

This fraction is a little harder to turn into a decimal, as sevenths make recurring decimals.

You can use a bus shelter division to work out the decimal or use a calculator. You should be able to this both ways. Certainly get used to using your calculator, but also remember that you will not always have one to hand, so it is important to be able to do the division by hand.

We have learned in prior examples that to turn a decimal into a percentage, we must multiply by $100$. To reverse the process, we must divide by $100$.