GCSE Maths Practice: decimals
This foundation-level GCSE Maths question helps you practise converting decimals to fractions. It focuses on understanding that each place value after the decimal point represents a power of ten.
When a decimal has one digit after the point, the denominator is 10. Two digits mean hundredths (100), and three mean thousandths (1000). Always simplify if possible.
Understanding the Concept
Decimals are another way of expressing fractions. Both show parts of a whole, but decimals use powers of ten. In GCSE Maths, being able to switch between the two helps you in many areas such as percentages, ratios, and measurements.
For instance, in the decimal 0.2, the digit 2 sits in the tenths place, representing two parts out of ten, or \(\frac{1}{5}\) when simplified. Similarly, 0.25 represents twenty-five hundredths, which simplifies to \(\frac{1}{4}\). Understanding this connection between decimals and fractions builds number fluency and supports higher-level reasoning.
Step-by-Step Conversion
- Count the number of digits after the decimal point. One digit means tenths, two means hundredths, and three means thousandths.
- Write the digits as the numerator and the corresponding power of ten as the denominator.
- Simplify the fraction by dividing both parts by their greatest common factor (GCF).
- Check your answer makes sense — the value should be smaller than one if the decimal is less than one.
Worked Examples
Example 1: Convert 0.2 to a fraction.
0.2 = \(\frac{2}{10}\) → simplify by 2 → \(\frac{1}{5}\).
Example 2: Convert 0.25 to a fraction.
0.25 = \(\frac{25}{100}\) → divide by 25 → \(\frac{1}{4}\).
Example 3: Convert 0.5 to a fraction.
0.5 = \(\frac{5}{10}\) → divide by 5 → \(\frac{1}{2}\).
Example 4: Convert 0.375 to a fraction.
0.375 = \(\frac{375}{1000}\) → divide by 125 → \(\frac{3}{8}\).
Common Mistakes
- Wrong denominator: Students sometimes use 100 instead of 10 for decimals with one place. Remember, the first place after the point always represents tenths.
- Skipping simplification: Fractions must be reduced to their lowest terms to earn full marks in exams.
- Confusing tenths and hundredths: Always count the number of decimal places carefully.
Real-Life Applications
Decimals appear constantly in everyday life. A shop might offer 20% off, which is equivalent to one fifth off the price — the same as the decimal 0.2. In measurements, 0.25 metres equals one quarter of a metre. In cooking, 0.5 kilograms means half a kilogram. Understanding how decimals link to fractions allows you to visualise sizes, portions, and discounts easily.
In science, decimals are often used for precision, while fractions show exact relationships. For example, a chemist may record 0.25 litres, which equals one quarter of a litre. Both forms represent the same value, and choosing between them depends on context.
FAQs
1. What does 0.2 mean in fraction form?
It represents two tenths, which simplifies to \(\frac{1}{5}\).
2. How can I tell what denominator to use?
Count the number of digits after the decimal point. Each position represents another power of ten.
3. Can I convert repeating decimals to fractions?
Yes, but you’ll need algebraic methods — these are covered in higher-tier GCSE questions.
4. Why simplify fractions?
It makes answers clearer, easier to compare, and required by exam marking schemes.
Study Tip
Practise by listing decimals between 0.1 and 1, converting each to a simplified fraction. For instance: 0.2 → 1/5, 0.25 → 1/4, 0.4 → 2/5, 0.5 → 1/2. Spot the patterns in how the numbers relate — this helps you move between fractions, decimals, and percentages confidently.
Once you master the relationship between decimals and fractions, you’ll find topics like percentages and ratio problems much easier. Remember — decimals are simply fractions written in another form.