GCSE Maths Practice: decimals

Question 7 of 10

This GCSE Maths foundation question helps you practise converting a one-place decimal into a fraction. Understanding this simple but important skill builds a strong base for future work with percentages, ratios, and proportion.

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\( \begin{array}{l}\textbf{Convert } 0.1 \textbf{ to a fraction in its simplest form.}\end{array} \)

Choose one option:

Link decimals to place value: one digit after the point means tenths, two digits mean hundredths, and three mean thousandths. Recognising this pattern helps you quickly convert between decimals and fractions.

Understanding Decimals and Fractions

Decimals and fractions are simply two different ways of expressing the same thing — parts of a whole. In GCSE Maths, being able to move smoothly between decimals and fractions helps you in topics such as percentages, ratio, proportion, and probability. When we write 0.1, the digit 1 sits in the tenths place. This means one out of ten equal parts, or \(\frac{1}{10}\).

The decimal point separates the whole numbers from the fractional part. The first digit to the right of the decimal point represents tenths, the second represents hundredths, and the third represents thousandths. Therefore:

  • 0.1 = one tenth = \(\frac{1}{10}\)
  • 0.01 = one hundredth = \(\frac{1}{100}\)
  • 0.001 = one thousandth = \(\frac{1}{1000}\)

Step-by-Step Conversion

  1. Identify how many digits appear after the decimal point. Here, there is one digit (1).
  2. One decimal place means tenths, so use 10 as the denominator.
  3. Write the number as \(\frac{1}{10}\).
  4. Check if the fraction can be simplified. It cannot — so this is the final form.

This quick, consistent method works for any terminating decimal.

Worked Examples

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

Example 2: Convert 0.4 to a fraction.
0.4 = \(\frac{4}{10}\) → simplify by 2 → \(\frac{2}{5}\).

Example 3: Convert 0.75 to a fraction.
0.75 = \(\frac{75}{100}\) → divide both by 25 → \(\frac{3}{4}\).

These examples show how the number of digits after the decimal determines the denominator and that simplifying is always the final step.

Common Mistakes

  • Writing 0.1 as \(\frac{1}{100}\): This happens when students forget that one decimal place means tenths, not hundredths.
  • Leaving fractions unsimplified: For example, writing 0.2 as \(\frac{2}{10}\) instead of \(\frac{1}{5}\).
  • Forgetting the meaning of place value: Always read the decimal aloud as 'one tenth', 'two tenths', etc., to avoid errors.

Real-Life Connections

Understanding decimals and fractions has real-world importance. If a shop offers a 10% discount, that’s one tenth of the total price — exactly what 0.1 represents. In measurements, 0.1 m equals one tenth of a metre, or 10 cm. When using money, £0.10 equals ten pence, which is one tenth of a pound. These everyday examples help you visualise why 0.1 corresponds to \(\frac{1}{10}\).

FAQs

1. Why is 0.1 equal to \(\frac{1}{10}\)?
Because the 1 is in the tenths place, meaning 1 divided by 10.

2. What happens if the decimal has two digits?
Then the denominator becomes 100. For instance, 0.25 = \(\frac{25}{100}\) = \(\frac{1}{4}\).

3. Can every decimal be written as a fraction?
All terminating decimals can. Some decimals, like 0.333…, repeat infinitely — they still have fractional forms, but you need algebra to find them.

Study Tip

When revising, create a small table showing decimals and their equivalent fractions up to hundredths and thousandths. Practise saying them aloud — for example, '0.1 is one tenth' or '0.01 is one hundredth.' This strengthens your place-value understanding and makes conversions automatic during exams.

Mastering the link between decimals and fractions will improve your overall number fluency, setting a strong foundation for ratio, proportion, and percentage questions across the GCSE Maths curriculum.