What is the value of the 6 in 4,678?
Look at the position of the digit.
The 6 is in the hundreds column, so its value is 600.
Place Value and Rounding
Place value determines the value of each digit depending on its position within a number. Rounding is used to simplify numbers and check whether answers are reasonable in GCSE Maths calculations.
Overview
In our number system, the value of a digit depends on its position.
For example, the digit 5 in 53 is worth 50, but the digit 5 in 0.5 is worth five tenths.
\( 4,582.67 \)
This number contains thousands, hundreds, tens, ones, tenths and hundredths.
Once you understand place value, rounding becomes much easier.
What you should understand after this topic
- Understand how the value of a digit depends on its place
- Read large numbers and decimals correctly
- Round to the nearest 10, 100 and 1000
- Round to decimal places
- Estimate answers sensibly
Key Definitions
Place Value
The value a digit has because of its position in the number.
Digit
Any single number from 0 to 9.
Decimal Point
The point that separates whole numbers from decimal parts.
Round
To write a number to a chosen level of accuracy.
Estimate
A close answer found by rounding before calculating.
Decimal Place
A position to the right of the decimal point, such as tenths or hundredths.
Key Rules
How to Solve
Step 1: Understand place value
Each place value column is 10 times bigger than the column to its right.
In \(4,582.673\), the 4 means 4000, the 5 means 500, and the 6 means 0.6.
Exam tip: Always check the position of the digit before giving its value.
Step 2: Read decimal place value
Digits after the decimal point represent tenths, hundredths and thousandths.
In \(3.742\), the 7 is in the tenths column.
So its value is \(0.7\).
Step 3: Round whole numbers
To round, look at the digit immediately to the right of the place value you need.
Round \(6,782\) to the nearest 100
Hundreds digit = 7.
Next digit = 8.
Since 8 is 5 or more, round up.
Answer: \(6,800\)
Step 4: Round decimals
Use the same rule for decimal places.
Round \(5.786\) to 2 decimal places
Hundredths digit = 8.
Next digit = 6.
Since 6 is 5 or more, round up.
Answer: \(5.79\)
Step 5: Know common rounding instructions
Nearest 10, 100, 1000
Used for whole numbers.
Decimal places
Used for decimal accuracy.
Significant figures
Used for large or small numbers.
Suitable accuracy
Used in real-life contexts.
Step 6: Watch for chains of 9s
Sometimes rounding affects more than one digit.
Round \(2.999\) to 2 decimal places
\(2.999 \approx 3.00\)
Exam tip: Keep the correct number of decimal places after rounding.
Step 7: Use rounding to estimate
Rounding can make calculations easier and help check answers.
\(49.8 \times 2.1 \approx 50 \times 2 = 100\)
See estimation for more rounding-based checks.
Step 8: Exam method summary
- Identify the required place value.
- Look at the digit immediately to the right.
- If it is 5 or more, round up.
- If it is 4 or less, keep the digit the same.
- Write the answer with the correct number of digits.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics.
Edexcel
Write down the value of the digit 8 in the number 58,204.
Edexcel
Write these numbers in order of size, starting with the smallest.
\( 0.8,\; 0.08,\; 0.808,\; 0.88 \)
Edexcel
Write the following numbers in order, starting with the smallest.
\( 4{,}503,\; 4{,}053,\; 4{,}530,\; 4{,}350 \)
Edexcel
Round 7,846 to the nearest 10.
Edexcel
Round 3.472 to 2 decimal places.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on numerical fluency and precise rounding skills.
AQA
Write down the value of the digit 5 in the number 3.504.
AQA
Round 6.749 to 1 decimal place.
AQA
Round 0.0786 to 2 significant figures.
AQA
A student says that 0.47 is greater than 0.5 because 47 is greater than 5.
Is the student correct?
Tick one box. Yes ☐ No ☐
Give a reason for your answer.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising place value understanding and accurate rounding.
OCR
Write down the value of the digit \(7\) in the number \(3721\).
OCR
Round 84,629 to the nearest thousand.
OCR
Round 5.0849 to 3 significant figures.
OCR
Here are four numbers.
\( 6{,}041 \qquad 6{,}401 \qquad 6{,}140 \qquad 6{,}104 \)
Write the numbers in order of size, starting with the largest.
Exam Checklist
Step 1
Identify the place you are rounding to.
Step 2
Look at the digit immediately to the right.
Step 3
Use the 0–4 down, 5–9 up rule.
Step 4
Check whether zeros are needed as placeholders.
Most common exam mistakes
Wrong place
Rounding to tenths instead of hundredths, or vice versa.
Wrong next digit
Looking too far right instead of just the next digit.
Zeros
Forgetting zeros when they show place value.
Estimation
Choosing rounded numbers that are not sensible.
Common Mistakes
These are common mistakes students make when working with place value and rounding in GCSE Maths.
Looking at the wrong digit
Incorrect
A student checks the wrong place value when rounding.
Correct
Always look at the digit immediately to the right of the place you are rounding to. This digit decides whether to round up or stay the same.
Mixing up place values
Incorrect
A student confuses tenths with hundredths or other positions.
Correct
Know the place values clearly: tenths (0.1), hundredths (0.01), thousandths (0.001). Identify the correct position before rounding.
Forgetting placeholder zeros
Incorrect
A student drops zeros that are needed to show place value.
Correct
Zeros can be important for showing accuracy. For example, 3.50 is not the same level of precision as 3.5.
Incorrect decimal rounding format
Incorrect
A student writes \(5.786\) to 2 decimal places as \(5.780\).
Correct
When rounding to 2 decimal places, the answer should have exactly two decimal digits. \(5.786\) becomes \(5.79\), not \(5.780\).
Not carrying when rounding up
Incorrect
A student rounds \(2.999\) incorrectly to \(2.99\).
Correct
Rounding may require carrying. \(2.999\) rounded to 2 decimal places becomes \(3.00\), not \(2.99\).
Try It Yourself
Practise understanding place value and rounding numbers appropriately.
Foundation
Foundation Practice
Identify place value and round to whole numbers and decimal places.
What is the value of the 3 in 2,345?
Count place values from right to left.
The 3 is in the hundreds place, so its value is 300.
Round 47 to the nearest 10.
Look at the ones digit.
7 is 5 or more, so round up to 50.
Round 62 to the nearest 10.
Look at the ones digit.
2 is less than 5, so round down to 60.
Round 3.67 to 1 decimal place.
Look at the second decimal place.
The second decimal is 7, so round up to 3.7.
Round 5.23 to 1 decimal place.
Check the second decimal digit.
3 is less than 5, so it rounds to 5.2.
Round 149 to the nearest 10.
Look at the ones digit.
9 rounds up, so 149 becomes 150.
Round 381 to the nearest 10.
Look at the ones digit.
1 is less than 5, so it rounds to 380.
A student rounds 2.45 to 2.4. What is wrong?
Check the digit after the rounding place.
5 rounds up, so 2.45 becomes 2.5.
Round 7.89 to the nearest whole number.
Look at the decimal part.
0.89 rounds up, so the answer is 8.
Higher
Higher Practice
Round to significant figures and estimate calculations.
Round 4,582 to 1 significant figure.
Keep the first non-zero digit.
4 is followed by 5, so round up to 5000.
Round 3,246 to 2 significant figures.
Keep first 2 digits.
32 stays, next digit is 4 so round down → 3200.
Round 0.0785 to 2 significant figures.
Ignore leading zeros.
First significant digits are 7 and 8, next is 5 so round up → 0.079.
Round 0.00436 to 2 significant figures.
Start counting from first non-zero digit.
Digits are 4 and 3, next is 6 so round up → 0.0044.
Estimate: 49 × 18
Round to 1 significant figure.
49 ≈ 50 and 18 ≈ 20 → 50 × 20 = 1000.
Estimate: 301 ÷ 6
Round to easy numbers.
301 ≈ 300 → 300 ÷ 6 = 50.
Round 7.995 to 2 decimal places.
Look at the third decimal place.
5 rounds up → 7.995 becomes 8.00.
Round 12,345 to 3 significant figures.
Keep first 3 digits.
123 stays, next digit is 4 so round down → 12300.
A student rounds 0.0567 to 2 significant figures and writes 0.05. What is wrong?
Look at the third significant digit.
0.0567 rounds to 0.057 (7 rounds up).
Estimate: 198 + 302
Round to nearest hundred.
198 ≈ 200 and 302 ≈ 300 → total is 500.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
How do I know which digit to round?
Look at the digit immediately to the right of the place value you are rounding to.
What happens if the next digit is 5 or more?
You round the number up.
Why is place value important?
It tells you the value of each digit, which is essential for accurate calculations and rounding.