Lesson

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.

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

Fraction | Decimal | Percentage |
---|---|---|

\dfrac{60}{100} |

Worked Solution

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.

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

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:

Outcome | Probabilty (Fraction) | Probability (Decimal) |
---|---|---|

\text{Purple} | \dfrac{3}{10} | 0.3 |

\text{Blue} | \dfrac{1}{5} | |

\text{Black} | \dfrac{1}{2} |

Worked Solution

b

What is the sum of the probabilities for each outcome?

Worked Solution

Idea summary

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

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

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

Write the number in decimal form.

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

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

b

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

Worked Solution

c

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

Worked Solution

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\%.

Describe probabilities using fractions, decimals and percentages