Decimal Expansion

We can expand a whole number like this:

So 563 is a sum of each digit multiplied by its Place Value (hundreds, tens, units).

We can also do this with a Decimal Number such as 37.29:

Here is how it looks after the multiplications:

37.29  =  30 + 7 + 0.2 + 0.09

Fractions

We can also do a decimal expansion of a fraction:

Sometimes the expansion goes forever:

These are called "repeating", "periodic" or "recurring" decimals, and can have repeating patterns like this:

We can show the repeating pattern by putting a line over it, like this:

It is also possible for some numbers to have an endless decimal expansion without repeating. They are called irrational numbers, are never fractions, and a famous example is π (Pi):