Free GCSE Maths lesson: Number

Free LessonsGCSE / Key Stage 4Maths → Place Value, Ordering and Comparing Numbers

Lesson 69 · GCSE / Key Stage 4 · Maths · Number

Place Value, Ordering and Comparing Numbers

Read, order and compare integers, decimals and large numbers using place value.

Qualification: GCSEKey Stage 4Subject: MathsStrand: Number

GCSE specification fit

Place Value, Ordering and Comparing Numbers is part of GCSE Maths Number.

Read, order and compare integers, decimals and large numbers using place value. Questions may ask you to compare values in different forms, explain inequality statements, use number lines or decide whether a rounded value is sensible.

QualificationGCSE Mathematics
Key stageKey Stage 4
StrandNumber
Tier guidanceFoundation and Higher

What you will learn

  • Use place value columns for whole numbers and decimals.
  • Compare positive and negative numbers accurately.
  • Order values written in different forms.
  • Use inequality symbols to compare quantities.
  • Explain the size of a number using digits and place value.
  • Check comparisons in context, including money, measures and rounded values.

Why this matters

Place value is the base layer for rounding, estimation, standard form, percentages, ratio and calculator checks.

Prior knowledge

You should already be comfortable with:

  • Counting in powers of 10.
  • Reading decimals.
  • Using a number line.
  • Basic inequality symbols.

Clear explanation

Main idea

Every digit has a value because of its position. In 4,307.52 the 3 means 300, the 7 means 7 ones, the 5 means 5 tenths and the 2 means 2 hundredths.

Method

To compare decimals, line up the decimal points and compare from left to right. Add placeholder zeros only to help reading; 0.7 and 0.70 are equal. If units differ, convert first, for example 1.2 m = 120 cm before comparing with 95 cm.

Exam tip

On a number line, numbers further right are larger. With negatives, -2 is greater than -5 because it is closer to zero. Rounded values can hide exact size, so read the question carefully before deciding whether two measurements are definitely equal.

Worked examples

Ordering decimals

Put 0.45, 0.5, 0.405 and 0.54 in ascending order.

Answer: Write as 0.450, 0.500, 0.405, 0.540, so the order is 0.405, 0.45, 0.5, 0.54.

Comparing negatives

Which is larger: -3.2 or -3.02?

Answer: -3.02 is larger because it is closer to zero.

Comparing with units

Which is longer: 0.84 m or 79 cm?

Answer: Convert first: 0.84 m = 84 cm, and 84 cm > 79 cm, so 0.84 m is longer.

Quick checks

Choose an answer, then check your thinking.

1. Which number is the smallest?

2. Which decimal place-value statement is true?

Practice questions

Question 1

A school prints 52,781 revision booklets. Write the value of the digit 7 in this number and name its place-value column.

Reveal answer and marking guidance

Answer: 700; the 7 is in the hundreds column.

Marking: Identify the hundreds column and give the digit value as 7 hundreds, not just the digit 7.

Question 2

Three athletes jump 0.63 m, 0.603 m and 0.36 m in a standing jump drill. Put the distances in ascending order.

Reveal answer and marking guidance

Answer: 0.36 m, 0.603 m, 0.63 m.

Marking: Line up decimals as 0.360, 0.603 and 0.630, then compare digit by digit and keep the units.

Question 3

At 6 am, one town is at −4°C and another is at −7°C. Which temperature is greater, and how would you justify it on a number line?

Reveal answer and marking guidance

Answer: −4°C is greater.

Marking: −4 is further right on the number line than −7, so it represents the warmer temperature.

Question 4

A video has 3.5 million views. Write this number in digits and explain the role of the zero placeholders.

Reveal answer and marking guidance

Answer: 3,500,000.

Marking: 3.5 million is 3 million plus 0.5 million, so the zeros hold the thousands, hundreds, tens and ones places.

Question 5

Put -1.08, -1.8, -0.18 and 0.018 in ascending order.

Reveal answer and marking guidance

Answer: -1.8, -1.08, -0.18, 0.018.

Marking: Use a number line: the most negative value is smallest, then compare the decimal places.

Question 6

Two screws are measured as 0.407 cm and 0.47 cm wide. Fill in the correct symbol: 0.407 ___ 0.47.

Reveal answer and marking guidance

Answer: 0.407 < 0.47.

Marking: Compare as 0.407 and 0.470; the tenths match but 0 hundredths is less than 7 hundredths.

Question 7

A desk is 1.2 m long and a shelf is 95 cm long. Which is larger?

Reveal answer and marking guidance

Answer: The 1.2 m desk is larger.

Marking: Convert first: 1.2 m = 120 cm, and 120 cm > 95 cm.

Question 8

A number rounded to one decimal place is 4.6. Could the original number have been 4.54?

Reveal answer and marking guidance

Answer: No.

Marking: 4.54 rounds to 4.5 to one decimal place; values from 4.55 up to 4.649... round to 4.6.

Question 9

Write the largest of these values: 0.609, 0.69, 0.6901 and 0.6099.

Reveal answer and marking guidance

Answer: 0.6901.

Marking: Compare as 0.6090, 0.6900, 0.6901 and 0.6099; 0.6901 is just larger than 0.6900.

Question 10

Order these race times from fastest to slowest: 12.405 s, 12.45 s, 12.4501 s and 12.399 s.

Reveal answer and marking guidance

Answer: 12.399 s, 12.405 s, 12.45 s, 12.4501 s.

Marking: Fastest means the smallest time. Compare as 12.3990, 12.4050, 12.4500 and 12.4501; trailing zeros help line up the decimal places but do not change the value.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For place-value questions, marks usually come from identifying the correct column value, lining up decimal points, ordering values from left to right on a number line, converting units before comparing and using inequality symbols the correct way round. In explanation questions, say which digit, position, unit conversion or rounding boundary decides the comparison.

Common mistakes

  • Treating longer decimals as larger: 0.603 is less than 0.63 because 0.603 = 0.603 and 0.63 = 0.630.
  • Forgetting how negatives order: -7 is smaller than -4 because it is further left on the number line.
  • Changing value with placeholder zeros: 0.7 and 0.70 are equal; zeros can help comparison but do not change the number.
  • Reading the wrong digit column: separate thousands, hundreds, tens, ones, tenths and hundredths before naming a digit value.

Extension challenge

Create five values using the digits 0, 3, 5 and 7, including one negative decimal and one number greater than one thousand. Put them in ascending order and explain the two comparisons that were easiest to get wrong.

Reveal answer

Example answer: A strong response lines up decimal points, handles the negative value using a number line and gives a clear reason for each inequality symbol.

Exam-board guidance

Place Value, Ordering and Comparing Numbers appears across GCSE Maths number work. The shared skill is to read the size of each number accurately before calculating, rounding or interpreting a context.

AQA GCSE Maths

Line up decimal places, compare from left to right, and be careful with negative numbers, rounded values and units on number lines.

OCR GCSE Maths

Show enough place-value working to justify ordering, especially when decimals have different numbers of digits or the values have units.

Pearson Edexcel GCSE Maths

Check whether values are integers, decimals, fractions, negatives or rounded measurements before deciding the comparison order.

Eduqas GCSE Maths

Use place-value columns or a number line when the question asks you to explain an ordering decision, especially with decimals or negatives.

WJEC Wales

Connect place-value comparisons to numeracy contexts such as money, measures and scales, and check that all values are in matching units.

CCEA GCSE Maths

Keep calculator and non-calculator expectations in mind; written comparison steps are useful on both unit styles, especially when negatives are involved.

Next lesson

Next, continue with Factors, Multiples and Divisibility.