Why is 342 different from 234, even though they use the same digits? Because in our number system, the place a digit sits in tells you what it is worth. Understanding place value is the key that unlocks big numbers, adding and subtracting in columns, and decimals later on. This lesson makes it clear.
The same digit, different worth
Our number system uses just ten digits (0–9), but a digit's value depends on its place. Reading from the right, the places are ones, then tens, then hundreds, and each place is worth ten times the one to its right.
So in 342, the 3 sits in the hundreds place and means 3 hundreds (300), the 4 is 4 tens (40), and the 2 is 2 ones. Altogether: 300 + 40 + 2 = 342.
In 342, the 3 means 300, the 4 means 40, and the 2 means 2.
Expanded form
Writing a number as the sum of what each digit is worth is called expanded form. It makes the place value visible: 506 = 500 + 0 + 6. Notice the zero in the tens place — it is a placeholder that says 'no tens', and it keeps the 5 in the hundreds place and the 6 in the ones place.
Zero is important: without it, 506 and 56 would look the same. The zero holds the place open.
Worked example
Write 274 in expanded form.
The 2 is in the hundreds place: 200.
The 7 is in the tens place: 70.
The 4 is in the ones place: 4.
Answer: 274 = 200 + 70 + 4
Why it matters
Place value is the reason column addition and subtraction work: you add ones to ones, tens to tens, and 'carry' to the next place when a column reaches ten. It is also how bigger places keep going — after hundreds come thousands, then ten-thousands, each ten times bigger.
Get place value solid and much of the maths ahead — big numbers, decimals, and column arithmetic — becomes far easier to understand.
Check yourself
Try these. Pick an answer to see whether it's right and why.
In the number 342, what is the 3 worth?
The 3 is in the hundreds place, so it is worth 3 hundreds, which is 300.
Each place is worth how much compared with the place to its right?
Moving one place to the left multiplies the value by ten: ones, tens, hundreds, thousands.
What is 506 in expanded form?
5 hundreds, 0 tens, 6 ones: 500 + 0 + 6. The zero holds the tens place.
Why is the 0 in 506 important?
The zero is a placeholder for 'no tens'; without it, the number would read 56.
What is the value of the 7 in 274?
The 7 sits in the tens place, so it is worth 7 tens, which is 70.
In a nutshell
A digit's value depends on its place: ones, tens, hundreds, each ten times the place to its right.
Expanded form shows the value of each digit, e.g. 342 = 300 + 40 + 2.
Zero is a placeholder that holds a place open, so 506 is not the same as 56.
Place value is why column arithmetic and bigger numbers work.
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