Mastering Place Value in KS3 Maths
31/05/2025 / TutorialsMastering Place Value in KS3 Maths
Introduction
Place value is one of the most fundamental concepts in mathematics. It helps us understand the value of each digit depending on its position in a number. A strong grasp of place value is essential for all areas of KS3 maths, from basic calculations to more complex topics like algebra and problem-solving.
This tutorial will guide KS3 students through understanding place value, working with large numbers and decimals, common mistakes to avoid, and applying this knowledge through examples and practice questions.
What is Place Value?
Place value tells us what a digit in a number is worth based on its position.
For example, in the number 4,582:
- The 4 is in the thousands place: 4 × 1,000 = 4,000
- The 5 is in the hundreds place: 5 × 100 = 500
- The 8 is in the tens place: 8 × 10 = 80
- The 2 is in the ones place: 2 × 1 = 2
Key Terms:
- Digit: A single number (0–9).
- Place: The position of the digit in a number.
- Value: What the digit is worth based on its place.
Understanding Larger Numbers
| Place | Value |
|---|---|
| Thousand | 1,000 |
| Ten Thousand | 10,000 |
| Hundred Thousand | 100,000 |
| Million | 1,000,000 |
| Ten Million | 10,000,000 |
| Hundred Million | 100,000,000 |
| Billion | 1,000,000,000 |
Worked Examples: Whole Numbers
Example 1: What is the value of the 9 in 392,847?
The 9 is in the ten thousands place.
9 × 10,000 = 90,000
Example 2: Write the number 4,700,218 in words.
Answer: Four million, seven hundred thousand, two hundred and eighteen.
Example 3: Which digit is in the hundred thousands place in 8,413,592?
Answer: 4
Example 4: Round 4,687,125 to the nearest million.
Look at the hundred thousands place: 6 (600,000).
Since 600,000 is more than half a million, we round up.
Answer: 5,000,000
Place Value with Decimals
| Place | Value |
|---|---|
| Tenths | 0.1 |
| Hundredths | 0.01 |
| Thousandths | 0.001 |
| Ten-thousandths | 0.0001 |
Worked Examples: Decimals
Example 5: What is the value of the 6 in 12.654?
The 6 is in the tenths place.
6 × 0.1 = 0.6
Example 6: Write the value of the 3 in 0.0387.
The 3 is in the hundredths place.
3 × 0.01 = 0.03
Example 7: Round 5.8769 to 2 decimal places.
Look at the thousandths place (6). Since 6 is greater than 5, round the hundredths place up.
Answer: 5.88
Example 8: Order the following numbers from smallest to largest: 0.45, 0.405, 0.054, 0.504
Answer: 0.054, 0.405, 0.45, 0.504
Common Mistakes in Place Value
- Mistaking value for digit: In 6,742, the digit 7 is not just ‘7’ — its value is 700.
- Misplacing zeros: Writing 4.5 as 4.05 changes the value significantly.
- Ignoring decimals: 0.5 and 0.50 are the same value, but the extra zero shows precision — important in contexts like money.
Why Place Value Matters
Without place value, we couldn’t:
- Understand how large or small a number is.
- Perform basic arithmetic operations.
- Read and write large numbers and decimals accurately.
- Work confidently with money, measurements, and data.
A clear understanding of place value is essential for future success in areas like algebra, ratios, and real-world problem-solving involving money and measurements.
Practice Questions
- What is the value of the 7 in 7,845?
- Write 56,032 in words.
- What is the value of the 4 in 5.478?
- Place the following numbers in order from smallest to largest: 0.41, 0.14, 0.4, 0.401
- Round 8,472 to the nearest hundred.
- Round 0.6598 to 2 decimal places.
- What digit is in the thousandths place in 0.3729?
Answers
- 7,000
- Fifty-six thousand and thirty-two
- 0.4 (4 tenths)
- 0.14, 0.4, 0.401, 0.41
- 8,500
- 0.66
- 2
Building Strong Foundations
Place value is a key skill that lays the groundwork for success in KS3 mathematics and beyond. Mastery of place value ensures that students can tackle larger concepts with confidence.
At Principal Tutors, we provide expert support to help students master foundational maths skills. Our tutors are fully UK-qualified school teachers with classroom experience, and we tailor our sessions to meet the needs of each student.
If you are looking for targeted support in KS3 Maths, explore our KS3 Maths services designed to help students achieve their full potential.
Take the Next Step
Want to strengthen your child’s understanding of place value and core number skills? Principal Tutors is here to help. Visit Principal Tutors to book a consultation and find the perfect tutor match — because every child deserves to thrive in maths.
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