Free GCSE Maths lesson: Number

Free LessonsGCSE / Key Stage 4Maths → Decimals and Place Value

Lesson 10 · GCSE / Key Stage 4 · Maths · Number

Decimals and Place Value

Learn how decimal digits work, how to compare decimals accurately and how to round them without losing the place value.

Qualification: GCSE Key Stage 4 Subject: Maths Strand: Number

GCSE specification fit

A core Number skill for calculation, rounding and problem solving.

Decimal place value is used when comparing numbers, rounding, estimating, working with money and measures, using standard form and checking answers.

QualificationGCSE Mathematics
Key stageKey Stage 4
StrandNumber
Tier guidanceFoundation and Higher

What you will learn

  • How to name the places after the decimal point.
  • How to identify the value of a decimal digit.
  • How to compare and order decimals reliably.
  • How to round decimals to decimal places and significant figures.
  • How to use decimal place value to estimate and check calculator answers.
  • Why zero placeholders can change the way a number is read or rounded.

Why this matters

Decimals appear throughout GCSE Maths: money, measurement, percentages, bounds, standard form, graphs, probability and calculator answers.

A small place-value mistake can make an answer ten times too big or ten times too small, so this is one of the habits that protects your marks.

Prior knowledge

You should already be comfortable with:

  • place value for whole numbers,
  • multiplying and dividing by 10, 100 and 1000,
  • tenths, hundredths and thousandths,
  • using <, > and = to compare numbers.

Clear explanation

Place value after the decimal point

Digits to the left of the decimal point are whole-number places. Digits to the right are parts of one whole.

42.375 4 tens, 2 ones, 3 tenths, 7 hundredths, 5 thousandths

The first digit after the decimal point is tenths, the second is hundredths and the third is thousandths.

Comparing decimals

Compare from left to right. If it helps, add zeros at the end so the numbers have the same number of decimal places.

0.7 = 0.700 0.68 = 0.680 0.7 is greater than 0.68 because 700 thousandths is greater than 680 thousandths.

Rounding decimals

To round a decimal, find the place you are keeping, then look at the next digit. If the next digit is 5 or more, round up. If it is 4 or less, keep the digit the same.

3.486 rounded to 2 decimal places is 3.49 3.486 rounded to 1 decimal place is 3.5

Decimal places and significant figures

Decimal places count digits after the decimal point. Significant figures count important digits from the first non-zero digit.

0.0479 to 2 decimal places = 0.05 0.0479 to 2 significant figures = 0.048

Worked examples

Example 1: What is the value of the 6 in 18.264?

The 6 is the second digit after the decimal point, so it is in the hundredths column.

6 hundredths = 0.06
Answer: 0.06.

Example 2: Put 0.54, 0.507, 0.59 and 0.5 in ascending order.

Add zeros so each number has three decimal places.

0.540, 0.507, 0.590, 0.500 0.500 < 0.507 < 0.540 < 0.590
Answer: 0.5, 0.507, 0.54, 0.59.

Example 3: Round 7.356 to 1 decimal place.

The tenths digit is 3. The next digit is 5, so round the tenths digit up.

7.356 ≈ 7.4
Answer: 7.4.

Quick checks

Choose an answer, then check your thinking.

1. In 5.308, what is the value of the 0?

2. Which number is the largest?

3. What is 4.965 rounded to 2 decimal places?

Practice questions

Question 1

Write the value of the 7 in 23.174.

Reveal answer and marking guidance

Answer: 0.07 or 7 hundredths.

Marking: The 7 is the second digit after the decimal point, so it is in the hundredths column.

Question 2

Write 0.6, 0.58, 0.607 and 0.059 in descending order.

Reveal answer and marking guidance

Answer: 0.607, 0.6, 0.58, 0.059.

Marking: Compare as 0.607, 0.600, 0.580 and 0.059.

Question 3

Round 12.748 to 1 decimal place.

Reveal answer and marking guidance

Answer: 12.7.

Marking: Keep the tenths digit. The next digit is 4, so do not round up.

Question 4

Round 0.03864 to 2 significant figures.

Reveal answer and marking guidance

Answer: 0.039.

Marking: The first two significant figures are 3 and 8. The next digit is 6, so 38 rounds to 39.

Question 5

A runner completes a race in 12.405 seconds. Write this time to 2 decimal places.

Reveal answer and marking guidance

Answer: 12.41 seconds.

Marking: Keep the hundredths digit and use the thousandths digit 5 to round up.

Question 6

Write 4.08, 4.8, 4.008 and 4.18 in ascending order.

Reveal answer and marking guidance

Answer: 4.008, 4.08, 4.18, 4.8.

Marking: Compare as 4.008, 4.080, 4.180 and 4.800 so the columns line up.

Question 7

A calculator shows 3.2 × 0.48 = 15.36. Explain why this cannot be correct and give the correct answer.

Reveal answer and marking guidance

Answer: It cannot be correct because 3.2 × 0.48 is less than 3.2 × 0.5, which is 1.6. The correct answer is 1.536.

Marking: Use estimation to spot the decimal-place error, then place the decimal point correctly.

Question 8

A shop price is £0.075 per gram. Write this price in pence per gram, rounded to 1 decimal place.

Reveal answer and marking guidance

Answer: 7.5 pence per gram.

Marking: £0.075 = 7.5p; no extra rounding changes the value to 1 decimal place.

Question 9

A calculator gives 18 ÷ 7 = 2.571428571. Write the answer to 3 significant figures and explain which digit decides the rounding.

Reveal answer and marking guidance

Answer: 2.57. The next digit after the first three significant figures is 1, so the 7 stays the same.

Marking: Count significant figures from the first non-zero digit: 2, 5 and 7. Use the following digit to decide whether to round up.

Question 10

A measurement is 0.6049 m. Write it to 3 decimal places and explain why the final zero is or is not needed.

Reveal answer and marking guidance

Answer: 0.605 m. The final zero is not needed because the rounded value has three digits after the decimal point: 6, 0 and 5.

Marking: Keep the thousandths place and use the next digit, 9, to round up. Check that the answer shows exactly 3 decimal places.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For decimals, marks usually come from lining up place-value columns carefully, using zero placeholders when comparing numbers, showing the digit that decides rounding, and keeping the requested accuracy and units in the final answer.

Common mistakes

  • Thinking more digits always means larger: 0.607 is larger than 0.59, but 0.059 is much smaller than both.
  • Ignoring zero placeholders: 0.6 and 0.600 have the same value, but placeholders can make comparison clearer.
  • Counting decimal places from the wrong side: decimal places are counted after the decimal point, from left to right.
  • Mixing decimal places and significant figures: 0.0479 to 2 decimal places and to 2 significant figures give different answers.

Extension challenge

Find a decimal number between 0.37 and 0.38 that rounds to 0.38 to 2 decimal places and to 0.4 to 1 decimal place.

Reveal answer

One possible answer: 0.375.

0.375 rounds to 0.38 to 2 decimal places because the thousandths digit is 5. It rounds to 0.4 to 1 decimal place because the hundredths digit is 7.

Exam-board guidance

Decimal place value is assessed across GCSE Maths because it underpins rounding, estimation, calculator checks, money, measures and percentages.

AQA GCSE Maths

Decimal place value supports rounding, estimation, standard form, measures and percentage questions; write enough digits to show the requested accuracy.

OCR GCSE Maths

Compare decimals column by column, use zero placeholders when helpful and round only after checking the exact accuracy named in the question.

Pearson Edexcel GCSE Maths

Show decimal place value clearly when ordering, rounding or deciding whether a calculator display has a sensible size and accuracy.

Eduqas GCSE Maths

Decimal place value helps you avoid mistakes when questions ask for comparison, rounding to a named accuracy, estimation or numerical reasoning in context.

WJEC Wales

Expect decimals in practical numeracy questions involving money, measurement and rates; keep units with rounded answers and avoid over-rounding early.

CCEA GCSE Maths

Decimals often connect to fractions, percentages, money and measurement questions, so check place value before choosing calculator or written methods.

Next lesson

Next, practise comparing negative numbers and reading inequality symbols.