Calculate Probabilities as Both Fractions and Decimals

How can we find the probability of getting a yellow card when drawing from the following cards at random?

Well, there are two yellow cards out of ten cards, so the probability of getting a yellow one is 2/10 = 1/5!

We often write probability as a fraction because that is how we calculate it.

But can we convert 1/5 (or 2/10) into anything else?

Yes, to decimals! There are many different ways we can convert 1/5 to a decimal:

- Divide 1 by 5 to get 0.2

- Recall 1/10 is one tenth, i.e. 0.1, so 2 tenths is 0.2

- Or even recall 1/5 is 0.2 if we really know our decimals!

Let's have a look at another example:

What would be the probability of drawing a red or a yellow card from these as a decimal?

Well, there are 2 + 1 = 3 red or yellow cards and 5 cards altogether.

So the probability of drawing a red or a yellow card at random is 3/5.

How can we convert 3/5 to a decimal?

One way is to get the denominator to be a power of 10 (e.g. 10, 100, 1000) to use our place values.

We can do this by multiplying both the numerator and the denominator by 2 to get:

3/5 = 6/10

Now we recognise 1/10 = one tenth = 0.1

So, 6/10 = six tenths = 6 x 1/10 = 6 x 0.1 = 0.6

Or we could divide 3 by 5 if you like dividing numbers! This will then also give us 0.6.

Let's try some questions!