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 showing fractions. Both represent parts of a whole number, but decimals use powers of ten to show how big or small the part is. In GCSE Maths, fluency in converting between decimals and fractions helps you move easily between topics like percentages, ratios, and measures.
In the decimal 0.1, the 1 is in the first place after the decimal point. The first place represents tenths, so 0.1 means one tenth — which is written as the fraction \(\frac{1}{10}\). The process works because the decimal system is based on powers of ten. Each place value to the right of the decimal point is ten times smaller than the one before it.
Step-by-Step Conversion
- Identify how many digits appear after the decimal point. In 0.1, there is one digit, so it’s in the tenths place.
- Write the decimal as a fraction over 10: \(\frac{1}{10}\).
- If the fraction can be simplified, divide the numerator and denominator by their greatest common factor (GCF). In this case, it’s already in simplest form.
- Check your answer makes sense — 0.1 is smaller than 1, and \(\frac{1}{10}\) is also smaller than 1, so the conversion is consistent.
Worked Examples
Example 1: Convert 0.4 to a fraction.
0.4 = \(\frac{4}{10}\) → simplify by 2 → \(\frac{2}{5}\).
Example 2: Convert 0.06 to a fraction.
0.06 = \(\frac{6}{100}\) → divide by 2 → \(\frac{3}{50}\).
Example 3: Convert 0.375 to a fraction.
0.375 = \(\frac{375}{1000}\) → divide by 125 → \(\frac{3}{8}\).
Example 4: Convert 0.25 to a fraction.
0.25 = \(\frac{25}{100}\) → divide by 25 → \(\frac{1}{4}\).
Common Mistakes
- Using the wrong denominator: Some students mistakenly write 0.1 as \(\frac{1}{100}\). Remember, one decimal place means tenths, not hundredths.
- Forgetting to simplify: Even simple decimals should be reduced to their lowest terms if possible.
- Mixing decimals and percentages: 0.1 means one tenth, while 10% also means one tenth — they’re equivalent, but don’t confuse the two notations.
Real-Life Applications
Decimals like 0.1 appear everywhere in everyday life. When measuring 0.1 metres, you’re measuring one tenth of a metre — that’s 10 centimetres. In money, £0.10 means one tenth of a pound, or 10 pence. In cooking, 0.1 kilograms is one tenth of a kilogram, or 100 grams. The same relationship between decimals and fractions helps you estimate quantities, calculate percentages, and compare values quickly.
In science and technology, decimals are used instead of fractions for precision. However, understanding how they relate gives you a deeper mathematical insight and helps you check your answers logically — especially in GCSE exams where both forms may appear.
FAQs
1. Why is 0.1 equal to \(\frac{1}{10}\)?
Because the 1 is in the tenths place, meaning it represents one part out of ten equal parts.
2. What does 0.01 mean?
It means one hundredth, which is \(\frac{1}{100}\).
3. Are 0.1 and 10% the same?
Yes. Percent means 'per hundred,' so 10% = 10/100 = 1/10 = 0.1.
4. Why should I simplify fractions?
Simplifying helps to present answers neatly and consistently, which is required in all GCSE exams.
Study Tip
Create a quick reference chart linking decimals, fractions, and percentages for common values: 0.1 = 1/10 = 10%, 0.25 = 1/4 = 25%, 0.5 = 1/2 = 50%. Keep practising these to strengthen your number fluency. Being able to instantly move between these forms saves time during your exam and helps you check for mistakes easily.
Understanding 0.1 as one tenth is a building block for everything from percentages to ratio reasoning — master this small step, and you’ll be far more confident tackling larger numerical problems in GCSE Maths.