Place Value

Write down the number 3472. Why is the "4" only worth 4? Wrong — it is worth 400.

A digit's worth depends on where it stands. That idea is called place value, and once it clicks, big numbers, decimals and column arithmetic all start making sense.

Every place has a name

For 3472, reading right to left:

Place	Digit	Means
Ones	2	2 × 1
Tens	7	7 × 10
Hundreds	4	4 × 100
Thousands	3	3 × 1000

So:

$3472 = 3 \times 1000 + 4 \times 100 + 7 \times 10 + 2 \times 1$

Each step left multiplies a digit's value by 10; each step right divides it by 10. This is also why 0 matters so much: 35, 305 and 350 are completely different numbers because the 0 holds a seat.

InteractiveNumber Expander

3,472

Read as：three thousand four hundred and seventy-two

Expanded form

3000 + 400 + 70 + 2

Expanded form: take the number apart

Writing a number as a sum of its place values is called expanded form:

$3400 = 3000 + 400$
$5060 = 5000 + 60$ (6 tens, 0 ones)
$9009 = 9000 + 9$ (the hundreds and tens places hold 0)

Expanded form explains how arithmetic works. For example $3472 + 2000$ just bumps the thousands digit from 3 to 5: the answer is $5472$ .

Common trap

Saying a zero and writing a zero are different jobs. $9009$ reads "nine thousand and nine" — the middle zeros aren't said aloud, but both must be written.

Base ten: carry when you hit ten

Why does each place only hold 0–9? Because we use base ten: when a place reaches 10, it tips over into the next place.

$9 + 1 = 10$ : the ones place resets, the tens place gets 1
$99 + 1 = 100$ : a chain of carries

Base ten isn't the only choice — computers use binary (carry at two), and clocks use base sixty. But the core idea, "each place is a power of the base", is universal.

Notice the pattern

$10 = 10^1$ , $100 = 10^2$ , $1000 = 10^3$ … the place at position $n$ (counting from 0) is worth $10^n$ .

Why place value is a big deal

Roman numerals needed a whole sentence for 3888: MMMDCCCLXXXVIII. Place value needs 4 digits. Better still:

Any size number is writable — with just ten symbols;
Arithmetic becomes mechanical — work place by place, carry or borrow;
It extends gracefully — step right of the point and you get 0.1, 0.01, …

Check yourself

Quick quiz

1. In 5821, what does the 8 stand for?
2. Which zero can NOT be removed without changing the value?
3. 5000 + 300 + 2 = ?