Being able to swap between fractions and decimals is a core maths skill you’ll use all the time. This guide covers everything you need to know about converting and ordering terminating decimals and fractions.
🛒 Shopping
Comparing prices and working out discounts.
🍳 Cooking
Scaling recipes up or down for different numbers of people.
📏 DIY
Measuring lengths and calculating materials.
📊 Data
Reading graphs in the news or sports results.
Fractions vs. Terminating Decimals
A fraction represents a part of a whole (e.g., $\frac{3}{4}$). A terminating decimal is another way to show this, but it has a finite number of digits and stops (e.g., 0.75). The key skill is being able to convert between these two forms.
How to Convert Between Fractions and Decimals
Fraction → Decimal
Method 1: Division (Universal)
Simply divide the numerator by the denominator. The fraction bar means “divided by”.
Example: $\frac{3}{8} = 3 \div 8 = 0.375$
Method 2: Equivalent Fractions
Multiply the top and bottom by the same number to make the denominator 10, 100, or 1000.
Example: $\frac{4}{5} \xrightarrow{\times 2} \frac{8}{10} = 0.8$
Decimal → Fraction
Step 1: Use Place Value
Write the decimal’s digits over its place value (10 for tenths, 100 for hundredths, etc.).
| H | T | U | . | 1/10 | 1/100 |
|---|---|---|---|---|---|
| 0 | . | 7 | 5 |
Example: The last digit of 0.75 is in the hundredths place, so it becomes $\frac{75}{100}$.
Step 2: Simplify
Divide the top and bottom by their highest common factor to find the simplest form.
Example: $\frac{75}{100} \xrightarrow{\div 25} \frac{3}{4}$
How to Order Fractions and Decimals
To order a mixed list of numbers, convert them all to the same format. Decimals are usually easiest.
Example: Order $\frac{1}{2}, 0.6, 0.65, \frac{3}{4}$
- Convert fractions to decimals: $\frac{1}{2} = 0.5$ and $\frac{3}{4} = 0.75$.
- Write the new list: 0.5, 0.6, 0.65, 0.75.
- Compare the decimals: The list is already in ascending order.
- Write the final answer using original numbers: $\frac{1}{2},\ 0.6,\ 0.65,\ \frac{3}{4}$.
Tutor Insights
🤔 Common Misunderstandings
- Dividing the wrong way: Always remember it’s top ÷ bottom!
- Forgetting to simplify: Questions almost always ask for the simplest form of a fraction.
- Comparing decimals of different lengths: Thinking 0.4 is smaller than 0.25. To avoid this, pad with zeros: 0.40 is clearly larger than 0.25.
📝 Common Exam Mistakes
- Not fully simplifying: Leaving $\frac{50}{100}$ instead of $\frac{1}{2}$ will lose marks.
- Simple calculation errors: Double-check your division, especially on non-calculator papers.
- Incorrect ordering: This usually happens from an incorrect conversion or misreading place value.
Practice Questions
- Convert $\frac{4}{5}$ to a decimal.
- Convert 0.85 to a fraction in its simplest form.
- Convert $\frac{1}{8}$ to a decimal.
- Order from smallest to largest: $0.7,\ \frac{3}{4},\ 0.72,\ \frac{2}{3}$.
- A recipe calls for 0.375 kg of flour. Express this as a fraction.
- Which is greater: $\frac{9}{16}$ or 0.55?
Show Answers
- 0.8
- $\frac{17}{20}$ (from $\frac{85}{100} \div \frac{5}{5}$)
- 0.125
- $\frac{2}{3},\ 0.7,\ 0.72,\ \frac{3}{4}$ (Conversions: $\frac{3}{4} = 0.75$, $\frac{2}{3} \approx 0.667$)
- $\frac{3}{8}$ kg (from $\frac{375}{1000} \xrightarrow{\div 125} \frac{3}{8}$)
- $\frac{9}{16}$ is greater (since $\frac{9}{16} = 0.5625 > 0.55$)
FAQs
Q: What’s the difference between a terminating and recurring decimal?
A: A terminating decimal stops (e.g., 0.25). A recurring decimal has digits that repeat infinitely (e.g., $0.333\ldots$). This guide focuses on terminating decimals.
Q: Do I always need to simplify fractions?
A: Yes, almost always! Unless a question tells you not to, always give your answer as a fraction in its simplest form. It’s considered good mathematical practice.
Need Help Converting Fractions and Decimals?
A qualified GCSE maths tutor can build your confidence with fractions, decimals, and every other topic on the syllabus — step by step.
Find a GCSE Maths Tutor
