 # 13.04 Probability with decimals and percentages

Lesson

## Ideas

Can you  convert  a fraction to a decimal and percentage? When finding a probability as a decimal or percentage, we can first find the  probability as a fraction  and then convert.

### Examples

#### Example 1

Convert between percentages, fractions and decimals to complete the table:

Worked Solution
Create a strategy

To convert fractions and decimals to percentages multiply by 100\%.

Apply the idea

To convert the fraction to a percentage:

To convert the fraction to a decimal:

Idea summary

To convert fractions and decimals to percentages multiply by 100\%.

To convert decimals to percentages multiplying by 100\% is the same as increasing the place value of each digit by two places, and attaching a \% symbol.

## Probability with decimals

Let's see how we can express the probability of something happening in decimals.

### Examples

#### Example 2

A box of star stickers has 6 purple stickers, 4 blue stickers and 10 black stickers.

a

Complete the following table showing the probability of randomly selecting each colour:

Worked Solution
Create a strategy

Convert each fraction to a decimal.

Apply the idea

To convert \dfrac{1}{5} and \dfrac{1}{2} to decimals we must first convert them to fractions out of 10.

b

What is the sum of the probabilities for each outcome?

Worked Solution
Create a strategy

Add the probabilities in the last column.

Apply the idea
Idea summary

To convert a fraction to a decimal where the denominator is not a power of 10:

1. Find a suitable number to multiply or divide the denominator by to make it a power of 10.

2. Multiply or divide both the numerator and denominator by this number.

3. Write the number in decimal form.

## Probability with percentages

We can also work out the probability of something happening using percentages. We'll use a calculator to help us this time.

### Examples

#### Example 3

The spinner below is spun.

a

What is the chance it lands on blue? Write your answer as a fraction in its simplest form.

Worked Solution
Create a strategy

The chance (probability) can be calculated by: \dfrac{\text{Number of blue parts}}{\text{Total number of parts}}

Apply the idea

There are 4 blue parts out of 10 parts.

b

What is the chance it lands on blue as a percentage?

Worked Solution
Create a strategy

Multiply both parts of the fraction, found in part (a), by a number that will make the denominator 100.

Apply the idea

5\times 20 = 100, so we need to multiply the numerator and denominator by 20.

c

What is the chance it lands on blue as a decimal?

Worked Solution
Create a strategy

Use a place value table to write the decimals.

Apply the idea

40 \% is the same as \dfrac{40}{100}. To put it in a place value table, put the 0 in the hundredths column, 4 in the tenths column, and use a 0 for a placeholder:

\text{Probability}=0.4

Idea summary

Decimals and percentages are another way to express numbers, so we can use them for probability as well. If something is unlikely, and only has a one in four chance of happening \left(\dfrac{1}{4}\right), we may wish to express the probability of it happening as 0.25 or 25\%.

### Outcomes

#### MA3-19SP

conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes