GCSE Maths Practice: decimals

Question 10 of 10

This question checks your understanding of how to compare decimals. Being able to tell which decimal is greater or smaller helps with ordering numbers, interpreting data, and estimating values in GCSE Maths.

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\( \begin{array}{l}\textbf{Which is greater: } 0.3 \textbf{ or } 0.25\textbf{?}\end{array} \)

Choose one option:

When comparing decimals, always align the decimal points and add zeros if needed to make them the same length. Compare digits from left to right until one is greater.

Comparing Decimals

Decimals represent parts of a whole using powers of ten. Comparing them correctly ensures you can order numbers and estimate values accurately. To compare decimals like 0.3 and 0.25, you need to line up the digits by their decimal points so that each place value matches.

Each digit has a specific value depending on its position. The first digit after the decimal point represents tenths, the second represents hundredths, and so on. By comparing digits in order, you can quickly determine which number is larger or smaller.

Step-by-Step Method

  1. Write the numbers vertically, aligning the decimal points.
  2. If one decimal has fewer digits, add zeros so they have the same number of places. For example, write 0.3 as 0.30.
  3. Compare the digits from left to right — start with tenths, then hundredths, then thousandths if needed.
  4. The number with the larger digit in the first place where they differ is the greater number.

Worked Examples

Example 1: Compare 0.4 and 0.35.
0.40 vs 0.35 → tenths equal (4 vs 3) → 0.4 is greater.

Example 2: Compare 0.67 and 0.7.
0.67 vs 0.70 → tenths equal, hundredths 7 vs 0 → 0.7 is greater.

Example 3: Compare 0.502 and 0.5.
0.502 vs 0.500 → tenths equal, hundredths equal, thousandths 2 vs 0 → 0.502 is greater.

Common Mistakes

  • Not lining up decimals: If you compare 0.3 and 0.25 without alignment, it’s easy to misread which is bigger.
  • Comparing digit length instead of value: A longer number like 0.125 isn’t always smaller or larger — focus on place value.
  • Ignoring zeros: Remember that 0.3 and 0.30 represent the same value. Zeros after the last non-zero digit don’t change the number.

Real-Life Applications

Comparing decimals helps in shopping, science, and finance. For example, comparing prices (£0.30 vs £0.25) shows which item costs more. In sports timing, comparing 9.84 s vs 9.87 s identifies the faster result. In recipes, 0.35 kg of sugar is slightly more than 0.3 kg.

Understanding decimals makes everyday problem-solving easier, especially when using calculators or spreadsheets, which display results in decimal form rather than fractions.

FAQs

1. Are 0.3 and 0.30 different?
No — they are the same. Adding a zero doesn’t change the value.

2. How do I compare decimals with different lengths?
Add zeros until both numbers have the same number of digits after the decimal.

3. Why not use fractions instead?
Sometimes fractions make size comparisons clearer, but decimals are often easier when working with money or measurements.

4. Can two decimals ever be equal but look different?
Yes — for example, 0.5 and 0.50 are equal, but the second has one extra zero for clarity.

Study Tip

When practising, write several decimals with the same number of digits: 0.2, 0.25, 0.3, 0.35, 0.4. Then order them from smallest to largest. Spotting the pattern builds quick intuition for comparing any decimals you meet in GCSE exams.

Being confident at comparing decimals improves accuracy across GCSE Maths — from ordering data to estimating percentages and interpreting graphs.