Place Value
The value of a digit depends on its position: ones, tens, hundreds and so on.
Key idea
The value of a digit depends on its position: ones, tens, hundreds and so on.
In depth
Our number system is positional: the same digit means different amounts depending on where it sits. Each place is worth ten times the place to its right (ones, tens, hundreds, thousands). A number is the sum of each digit times its place value, and 0 holds a place open.
Worked example
In 4,305, the 4 is 4×1000, the 3 is 3×100, the 0 means no tens, and the 5 is 5×1. So 4305 = 4000 + 300 + 0 + 5.
Formula
Real-world uses
- Reading prices and measurements such as £4,305 or 2.75 kg
- Understanding calculator and spreadsheet displays
Common mistake
Forgetting the zero placeholder. 435 and 4,305 differ only by a 0, but they are very different sizes.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Place Value?
The value of a digit depends on its position: ones, tens, hundreds and so on. It is a topic at the beginner level in Arithmetic & Number Sense.
What is the formula for Place Value?
The key formula is 345 = 3×100 + 4×10 + 5×1.
Where is Place Value used in real life?
Real-world examples: Reading prices and measurements such as £4,305 or 2.75 kg; Understanding calculator and spreadsheet displays.
What should I learn before Place Value?
Make sure you are comfortable with Counting & Cardinality, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Place Value?
Forgetting the zero placeholder. 435 and 4,305 differ only by a 0, but they are very different sizes.
How can I practise Place Value?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Place Value?
Move on to Number Line next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.
- Skip Counting – Counting forward by a fixed step such as 2s, 5s or 10s; the root of multiplication.