Our number system (the Hindu-Arabic system) is a base ten, place value system. In a place value system, the value of a digit depends on its place in the number. For example, the digit 2 contributes 2 hundred to the number 1256, whereas it contributes 2 thousands to the number 2156.
Some numeration systems do not have place value. For example in the Roman numerals, 2 tens is XX and 2 hundreds is CC. The same symbol is not used in different places.
We think it is essential that place value columns are fully understood by everyone!
Just one digit (0-9) can be placed in a column
The central column is called "ones" and we need to know where it is!(Hence the decimal point)
Every column is ten times larger than its neighbour on the right (base ten property)
Every column is one tenth as large as its neighbour on the left (base ten property)
The total value of a number is the sum of the contributions due to each digit in its place value column:
3264 = 3 thousands + 2 hundreds + 6 tens + 4 ones
705 = 7 hundreds + 0 tens + 5 ones
8.3 = 8 ones + 3 tenths
8.32 = 8 ones + 3 tenths + 2 hundredths
8.328 = 8 ones + 3 tenths + 2 hundredths + 8 thousandths
Note how the contribution that the digit 3 makes in 8.3, 8.32 and 8.328 does not change!