Skip to content
VirtusAcademy

Ordering Decimals

FoundationChallengeAQAEdexcelOCR

Master ordering decimals for GCSE Maths with structured, exam-style practice. This Foundation resource covers ordering decimals and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Compare decimals digit by digit from the left — 0.45 is larger than 0.4.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Challenge / Extension

Stretch yourself beyond the basics.

WorksheetChallenge · PDFMark SchemeChallenge · PDF

Topic overview

Ordering decimals means arranging them by size, and the reliable method is to compare column by column rather than by how many digits each has.

The common trap is thinking a longer decimal must be larger. \(0.65\) has more digits than \(0.7\) but is smaller, because seven tenths beats six tenths regardless of what follows.

Padding with trailing zeros removes the difficulty entirely. Writing every number with the same number of decimal places lets you compare them almost as if they were whole numbers, and it costs only a moment.

Revision notes

Comparing column by column

Start with the largest place value and work right. The first column where the digits differ decides the order.

For \(0.72\) and \(0.69\), the tenths are \(7\) and \(6\), so \(0.72\) is larger and the hundredths never matter.

Padding with zeros

Give every number the same number of decimal places by adding trailing zeros, which does not change any value.

So \(0.4\), \(0.35\) and \(0.406\) become \(0.400\), \(0.350\) and \(0.406\), making the order immediately clear.

Ordering with negatives

Negative decimals order in reverse: the further from zero, the smaller.

So \(-0.8 < -0.3 < 0.2\). Sketching a number line makes this obvious and prevents the usual mistake.

Key points

  • Compare the largest place value first.
  • The first differing column decides the order.
  • More digits does not mean a larger number.
  • Pad with trailing zeros so all have the same length.
  • Ascending means smallest first.
  • Negative decimals order in reverse.

Worked examples

Example 1

Put \(0.5\), \(0.45\) and \(0.503\) in ascending order.

Working

\[0.500,\ 0.450,\ 0.503\]pad each to three decimal places
\[0.450 < 0.500 < 0.503\]compare column by column
\[0.45,\ 0.5,\ 0.503\]write the original numbers in order

Example 2

Which is larger, \(0.6\) or \(0.59\)?

Working

\[0.60 \text{ and } 0.59\]pad to the same number of decimal places
\[6 > 5 \text{ in the tenths column}\]compare the first differing column
\[0.6 \text{ is larger}\]state the conclusion

Example 3

Put \(-0.4\), \(0.1\) and \(-0.75\) in ascending order.

Working

\[-0.75 \text{ is furthest left on the number line}\]negatives order in reverse
\[-0.75 < -0.4 < 0.1\]arrange from smallest to largest

Common mistakes

  • Judging size by the number of digits.

    0.45 has more digits than 0.5 but is smaller. Compare place values, not lengths.

  • Comparing without padding.

    It is easy to misread 0.4 against 0.406. Adding zeros makes the comparison mechanical.

  • Treating negative decimals like positives.

    −0.75 is smaller than −0.4, even though 75 is bigger than 4.

  • Giving the answer in the padded form.

    Write the original numbers in your final answer, not 0.400.

Exam tips

  • Pad every number to the same number of decimal places first.
  • Compare from the left and stop at the first difference.
  • Sketch a number line whenever negatives are involved.
  • Check whether the question wants ascending or descending order.

Key terms

Ascending order
Arranged from smallest to largest.
Descending order
Arranged from largest to smallest.
Place value
The value of a digit determined by its column.
Trailing zero
A zero added after a decimal that does not change its value.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.