## Place value

Every digit in a number has its **place value**.

**Place value** is the value represented by a digit in a number on the basis of its position in the number. Each number keeps this order of positions:

1783645:

5 - ones

4 - tens

6 - hundreds

3 - thousands

8 - ten thousands

7 - hundred thousands

1 - millions

The place value of a digit increases by 10 times for every position we move left, e.g.:

2973:

place value of 3 is 3

place value of 7 is 7×10=70

place value of 9 is 9×10×10=900

place value of 2 is 2×10×10×10=2000

Due to this we can write every number in **expanded form**:

$$2973=3×1+7×10+9×100+2×1000$$

This system of number notation is called **decimal system** because it uses 10 digits (0, 1, 2 ... 9) to express numbers. Each place value in a number is a power of $10: 10^0 (=1), 10^1 (=10), 10^2 (=100), 10^3 (=1000), 10^4 (=10000)$, etc.

$$2973=$$

$$=3×10^0+7×10^1+9×10^2+2×10^3$$