Number - Fractions, decimals and percentages: work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8) (Foundation tier)

The idea

This skill is required for the Foundation tier. A terminating decimal has a finite number of digits. To convert it to a fraction, use the place value of the final digit for the denominator. For example, 0.375 ends in the thousandths column, so it is written as 375/1000, which simplifies to 3/8 by dividing the numerator and denominator by their highest common factor, 125. To convert a fraction to a decimal, either divide the numerator by the denominator (e.g., 3 ÷ 8) or, if possible, scale the fraction to have a denominator of 10, 100, or 1000 (e.g., 7/2 = 35/10 = 3.5). A fraction in its simplest form will only terminate if its denominator's prime factors are just 2s and 5s. Exam questions often require ordering a mix of decimals and fractions.

What earns the marks

• Writing the decimal over the correct power of ten, such as 375/1000 for 0.375, even if the cancelling is then incorrect.
• Cancelling by a correct common factor to reach the simplest form.
• Setting out a short division correctly when converting a fraction to a decimal, even if a calculation error is made.
• Writing the final value in the form the question asked for, whether decimal or fraction.

Common mistakes and how to put them right

• Writing 0.375 as 375/100 instead of 375/1000.

  Put it right: Count the decimal places carefully; three places means the denominator is 1000.

• Stopping at 375/1000 when the question asks for the simplest form.

  Put it right: Check if the numerator and denominator share common factors.

• Reading 3.5 as 3/5 rather than as three and a half (7/2).

  Put it right: The number before the decimal point is a whole number.

• Dividing the denominator by the numerator, so turning 3/8 into 8 ÷ 3 = 2.666..

  Put it right: Of 3 ÷ 8 = 0.375. Correction: The fraction bar means divide the top by the bottom.

Exam tips

• Learn common conversions by heart, such as 1/8 = 0.125, 1/4 = 0.25, and 3/4 = 0.75, to save time in non-calculator questions.
• Check a conversion by multiplying back: if you found 3/8 = 0.375, check that 0.375 × 8 = 3.
• When ordering a list of mixed decimals and fractions, it is usually easiest to convert everything to decimals first, order them, then write the answer using the original numbers.