Fractions decimals and percentages

Quick answer

Percentages are another way to show parts of a whole, like fractions and decimals. You can change percentages into fractions or decimals and back again. For example, 50% means 50 out of 100, which is the same as 0.5 or ½.

Learning outcome

By the end of this page, you will be able to convert between percentages, fractions, and decimals using simple steps and real-life examples.

• You can change a percentage into a decimal by dividing by 100.
• You can change a percentage into a fraction by writing it over 100 and simplifying.
• You can change a decimal or fraction into a percentage by multiplying by 100.
• You can use percentages in everyday situations like sharing food, calculating discounts, or measuring ingredients.

Why this matters

Understanding percentages helps you in many real-life situations. When you go shopping and see a 25% discount on a toy, you need to know how much money you save. When you cook and a recipe says to use ½ a cup of sugar, you might also see it written as 50% of a cup. Percentages are used in sports for scoring, in maps for distances, in money for interest, and in science for measurements. Knowing how to change between percentages, fractions, and decimals makes you more confident with numbers!

How it works

Percentages mean "per hundred". The word "percent" comes from "per cent" which means "per hundred". So 25% means 25 out of 100. This is the same as the fraction 25/100 or the decimal 0.25.

Here's how to change between them:

1. From percentage to decimal: Divide the percentage by 100.
2. From percentage to fraction: Write the percentage as a fraction over 100, then simplify.
3. From decimal or fraction to percentage: Multiply by 100.

Examples you can see

Let's look at some simple examples you can imagine or draw.

Example 1: What is 25% as a decimal?

• 25 ÷ 100 = 0.25

Example 2: What is 75% as a fraction?

• 75/100
• Simplify by dividing both by 25: 75 ÷ 25 = 3, 100 ÷ 25 = 4
• So 75% = 3/4

Example 3: What is 0.6 as a percentage?

• 0.6 × 100 = 60%

Example 4: What is ½ as a percentage?

• ½ = 0.5
• 0.5 × 100 = 50%

Try it as a mini adventure

Imagine you are a treasure hunter and you find a map that shows a chest buried at 75% of the way along a path. You also see a note that says the chest is at 3/4 of the path. Are these the same? Let's check!

1. 75% as a decimal = 75 ÷ 100 = 0.75
2. 3/4 as a decimal = 3 ÷ 4 = 0.75
3. They are the same! The treasure is at 0.75 of the path.

Now, let's say you find a recipe that calls for 20% of a cup of sugar. How much is that in fractions?

1. 20% = 20/100
2. 20 ÷ 20 = 1, 100 ÷ 20 = 5
3. So 20% = 1/5 of a cup

Common mistakes

• Mistake: Thinking 50% = 0.500 instead of 0.5
• Why it happens: Confusing the decimal point with extra zeros
• Fix: Remember that 0.5 and 0.500 are the same, but we usually write 0.5

• Mistake: Converting 1/4 to percentage by multiplying by 10 instead of 100
• Why it happens: Forgetting that percentages are "per hundred"
• Fix: Always multiply by 100 to get a percentage

• Mistake: Writing 100% as 100 instead of 1
• Why it happens: Not understanding that 100% means the whole
• Fix: 100% = 1 whole = 1.0 = 1

Parent and carer guide

Helping your child understand percentages doesn’t need to be hard! Here are 5 simple ways to make it fun:

1. Use everyday examples: When cooking, talk about ½ a cup or 25% of a recipe.
2. Play a game: Ask your child to find 50% of 20 cookies or 10% of 100 stickers.
3. Use a calculator: Let them check their answers to make sure they're right.
4. Make it visual: Draw circles or rectangles and split them into parts to show percentages.
5. Be patient: If they make a mistake, gently guide them to the right answer instead of saying "wrong".

Remember: The goal is understanding, not speed. Let your child explore and make mistakes—they’re part of learning!

Practice questions

1. What is 40% as a decimal?
2. What is 60% as a fraction?
3. What is 0.3 as a percentage?
4. What is ¼ as a percentage?
5. What is 80% as a decimal?
6. What is 1/5 as a percentage?
7. What is 0.75 as a percentage?
8. What is 90% as a fraction?
9. What is 0.1 as a percentage?
10. What is 3/10 as a percentage?

Answers:

1. 0.4
2. 3/5
3. 30%
4. 25%
5. 0.8
6. 20%
7. 75%
8. 9/10
9. 10%
10. 30%

FAQ

What does percentage mean?

Percentage means "per hundred". It’s a way to show how big or small something is compared to 100.

How do I change a percentage into a decimal?

Divide the percentage by 100. For example, 25% = 25 ÷ 100 = 0.25.

How do I change a fraction into a percentage?

First change the fraction into a decimal, then multiply by 100. For example, ½ = 0.5 = 50%.

Why are percentages useful?

Percentages help us compare parts of a whole, like discounts, test scores, and cooking recipes.

Can I use a calculator for percentages?

Yes! A calculator can help you check your answers. But it's good to understand the steps too.