Decimal numbers

Decimal numbers such as 3.14 are used in situations in which we look for more precision than whole numbers provide. As with whole numbers, a digit in a decimal number has a value which depends on the place of the digit.

In the number 3.14, 3 is called the whole number portion and 14 is called the decimal portion.

There are different types of decimal numbers:
- Exact decimals or regular numbers: they are the ones which don’t go on forever, so you can write down all their digits. For example: 0.125
- Repeating or recurring decimals: They are decimal numbers which at some point become periodic (repeated over and over). For example: 0.125252525252525... is a recurring decimal, where '25' is repeated forever. The group of repeated decimal digits is called period. There are two types:
· Pure periodic decimals: 3.1212121212…
· Eventually periodic decimals: 4.0312222222…..
- Irrational numbers: with no period, as p = 3.14159265…

Exercise: classify these numbers:

a) 1,23232323...

b) 1.356565656...

c) 1.234567891011...

d) 3.18

Solutions: a) Pure periodic decimal; b) Eventually periodic decimal; c) Irrational number; d) Exact decimal