fractions
Fractions and decimals
Connect tenths, hundredths and common equivalents.
Quick answer
Fractions and decimals are two ways of showing parts of a whole number. They can be connected and converted into each other. For example, one-tenth (1/10) is the same as 0.1, and one-hundredth (1/100) is the same as 0.01.Learning outcome
By the end of this page, you will understand how to connect tenths and hundredths in fractions and decimals, and you will be able to match common fraction and decimal equivalents. You will be able to:- Recognise that 1/10 = 0.1 and 1/100 = 0.01
- Match common fractions like 1/2, 1/4, 3/4 with their decimal equivalents
- Convert simple decimals to fractions and vice versa
- Use tenths and hundredths in everyday situations like money and measurements
Why this matters
Understanding fractions and decimals helps you solve problems in many everyday situations. Whether you're sharing a pizza, measuring ingredients for a recipe, or counting money, knowing how to work with parts of numbers makes life easier. Fractions and decimals are used in cooking, shopping, sports, time, and even games. When you understand them, you can make better choices and solve problems more quickly.How it works
Fractions and decimals are two different ways of showing the same part of a whole. A fraction shows how many parts you have out of a total number of equal parts. A decimal shows how many parts of a whole are in tenths or hundredths. Let's break it down: 1. Fractions are written with a top number (numerator) and bottom number (denominator). For example, in 3/4, the 3 is the number of parts you have, and 4 is the number of equal parts the whole is divided into. 2. Decimals use a decimal point to show parts of a whole. For example, 0.3 means 3 parts out of 10 equal parts. 3. Tenths are parts of a whole that are divided into 10 equal parts. In decimals, this is shown as one digit after the decimal point. 4. Hundredths are parts of a whole that are divided into 100 equal parts. In decimals, this is shown as two digits after the decimal point. 5. Equivalent values are different ways of showing the same amount. For example, 1/2 = 0.5, 1/4 = 0.25, and 3/4 = 0.75.Examples you can see
Let's look at some examples to help you understand how fractions and decimals work together. Example 1: Tenths Imagine you have a chocolate bar cut into 10 equal pieces. If you eat 3 pieces, you have eaten 3 out of 10 pieces. This is shown as 3/10 in fraction form or 0.3 in decimal form.| Fraction | Decimal |
|---|---|
| 1/10 | 0.1 |
| 2/10 | 0.2 |
| 3/10 | 0.3 |
| 4/10 | 0.4 |
| 5/10 | 0.5 |
| 6/10 | 0.6 |
| 7/10 | 0.7 |
| 8/10 | 0.8 |
| 9/10 | 0.9 |
| 10/10 | 1.0 |
| Fraction | Decimal |
|---|---|
| 1/100 | 0.01 |
| 10/100 | 0.10 |
| 25/100 | 0.25 |
| 50/100 | 0.50 |
| 75/100 | 0.75 |
| 100/100 | 1.00 |
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 2/4 | 0.5 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 2/5 | 0.4 |
| 3/5 | 0.6 |
| 4/5 | 0.8 |
Try it as a mini adventure
Adventure: The Fraction and Decimal Treasure Hunt You are on a treasure hunt in a magical garden where everything is measured in fractions and decimals! You need to find the treasure by solving clues that involve matching fractions and decimals. 1st time: You find a clue that says "One-tenth of the garden is a rose patch. What is this as a decimal?" Answer: 0.1 2nd time: You come across a pond with 100 lily pads. You see 25 lily pads that are blooming. What fraction of the lily pads are blooming? What is this as a decimal? Answer: 25/100 = 0.25 3rd time: You find a path that is 0.75 of the way to the treasure. What fraction of the path is this? Answer: 3/4 4th time: You see a sign that says "One-half of the apples are red." What is this as a decimal? Answer: 0.5 5th time: You discover a garden gate with 100 flowers. 10 of them are yellow. What fraction is this? What is it as a decimal? Answer: 10/100 = 0.10Common mistakes
- Mistake: Thinking that 0.1 is the same as 1/100.
Why it happens: Confusing the decimal place values.
Fix: Remember that 0.1 means one-tenth, which is 1/10, not 1/100. - Mistake: Mixing up the decimal places when converting fractions to decimals.
Why it happens: Not understanding how many digits are needed for tenths and hundredths.
Fix: Use a place value chart or draw a grid to help you see the correct decimal. - Mistake: Forgetting that 1/2 = 0.5, and thinking it's 0.2 or 0.05.
Why it happens: Not knowing common equivalents.
Fix: Practice with visual models or use a number line to see where 1/2 is. - Mistake: Writing 0.25 as 25/10 instead of 25/100.
Why it happens: Not understanding that hundredths have two decimal places.
Fix: Remember that 0.25 means 25 hundredths, so it's 25/100.
Parent and carer guide
Helping your child understand fractions and decimals can be fun and practical! Here are some ways to support them:- Use real-life examples: When cooking, ask your child to measure ingredients. For example, if a recipe calls for 1/2 a cup of sugar, ask them to find 0.5 of a cup.
- Play games: Use board games or apps that involve fractions and decimals to make learning interactive.
- Draw and model: Draw circles or rectangles and split them into equal parts. Ask your child to show 0.25 or 1/4 of the shape.
- Practice together: Make flashcards with fractions and decimals and quiz each other.
- Be patient: Some children may need more time to grasp the connection between fractions and decimals. Encourage practice and celebrate small wins.
Practice questions
- What is 1/10 as a decimal?
Answer: 0.1 - What is 50/100 as a decimal?
Answer: 0.50 - What is 0.25 as a fraction?
Answer: 25/100 - What is 1/4 as a decimal?
Answer: 0.25 - What is 0.7 as a fraction?
Answer: 7/10 - What is 3/4 as a decimal?
Answer: 0.75 - What is 1/5 as a decimal?
Answer: 0.2 - What is 0.30 as a fraction?
Answer: 30/100 - What is 0.01 as a fraction?
Answer: 1/100 - What is 4/5 as a decimal?
Answer: 0.8
FAQ
What is the difference between a fraction and a decimal?
Fractions show parts of a whole using a numerator and denominator, while decimals use a decimal point to show parts of a whole in tenths or hundredths.
How do I convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3 divided by 4 equals 0.75.
Why do we need to know fractions and decimals?
Fractions and decimals help us measure, share, and compare parts of a whole in everyday life, like cooking, shopping, and telling time.
Can all fractions be turned into decimals?
Yes, all fractions can be converted to decimals by dividing the numerator by the denominator.
What are some common fraction and decimal equivalents?
Some common ones are 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, and 1/10 = 0.1.