GCSE Maths Practice: decimals

Understanding Decimals with Three Places

Decimals such as 0.125, 0.375, and 0.625 represent parts of a whole that can be written as fractions over 1000. Every digit’s position after the decimal shows its place value — tenths, hundredths, and thousandths. Recognising this pattern helps convert any terminating decimal into a clear, simplified fraction.

For example, 0.375 means three hundred seventy-five thousandths, which equals \(\frac{375}{1000}\). By simplifying through division, we reduce it to a fraction with a smaller denominator that expresses the same value.

Step-by-Step Method

1. Write down the decimal number clearly.
2. Count the number of digits after the decimal point. Each digit adds a zero to the denominator: one → 10, two → 100, three → 1000.
3. Write the digits as the numerator and the matching power of ten as the denominator.
4. Find the highest common factor (HCF) and divide both parts by it.
5. Simplify until no further reduction is possible.

For instance, a decimal such as 0.625 becomes \(\frac{625}{1000}\), which simplifies to \(\frac{5}{8}\). The same steps work for any finite decimal, whether short or long.

Worked Examples

Example 1: Convert 0.25 to a fraction.
0.25 = \(\frac{25}{100}\) → divide both by 25 → \(\frac{1}{4}\).

Example 2: Convert 0.375 to a fraction.
0.375 = \(\frac{375}{1000}\) → divide both by 125 → \(\frac{3}{8}\).

Example 3: Convert 0.2 to a fraction.
0.2 = \(\frac{2}{10}\) → divide by 2 → \(\frac{1}{5}\).

Example 4: Convert 0.45 to a fraction.
0.45 = \(\frac{45}{100}\) → divide by 5 → \(\frac{9}{20}\).

Each example demonstrates how counting decimal places determines the denominator and simplification reduces the fraction to its lowest form.

Common Mistakes

• Incorrect denominator: Decimals with three digits require a denominator of 1000, not 100.
• Forgetting simplification: Leaving fractions like \(\frac{250}{1000}\) instead of \(\frac{1}{4}\) results in incomplete answers.
• Digit confusion: Mixing up 0.125 and 0.0125 changes the place value completely. Always check how many digits follow the decimal point.

Real-Life Connections

Decimals with three digits often appear in science, finance, and engineering. For example, £0.375 represents 37.5 pence, which equals \(\frac{3}{8}\) of a pound. A carpenter cutting a 1-metre plank into eight equal parts will measure roughly 0.125 metres per section. In recipes, 0.625 litres of milk represents five-eighths of a litre. Converting between these forms helps in estimation and accurate measurement.

FAQs

1. How do I know when to use 1000 as the denominator?
Count the decimal digits. Three digits after the point mean thousandths, so use 1000.

2. Why simplify fractions?
It provides the cleanest form and makes comparison between numbers easier, which exam markers require.

3. What about repeating decimals?
They can still be converted into fractions but require algebraic manipulation, covered in higher-level GCSE topics.

4. Is 0.125 close to one tenth?
Yes — it’s slightly larger. Estimating in this way helps check your answers quickly during exams.

Study Tip

Group your practice decimals into categories: one-place (0.2, 0.4), two-place (0.25, 0.75), and three-place (0.125, 0.375, 0.625). Converting each to a fraction will reveal patterns — many simplify into halves, quarters, or eighths. Recognising these makes future conversions almost automatic.

Understanding decimals to three places builds your foundation for ratio, percentages, and problem-solving across the GCSE Maths curriculum. Keep practising — the more patterns you see, the faster you’ll become at simplifying fractions confidently.