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, ones).
We can also do this with a Decimal Number such as 37.29:
Here's how it looks after the multiplications:
37.29 = 30 + 7 + 0.2 + 0.09
And that's decimal expansion!
Watch out for the "ths"!
Don't confuse Tens (10) with Tenths (110),
or Hundreds (100) with Hundredths (1100). The "ths" means it is a fraction!
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):