# Basic Math Terminology

## The Decimal System

The decimal system, sometimes referred to as base 10, contains a total of ten identifiers called digits. The decimal system is widely used because humans generally have ten fingers on which to count. For now, we will disregard other number systems for the sake of simplicity with the understanding that the decimal system is not unique.

The ten digits of the decimal system, arranged from lowest to greatest, are:

• 0 (zero)
• 1 (one)
• 2 (two)
• 3 (three)
• 4 (four)
• 5 (five)
• 6 (six)
• 7 (seven)
• 8 (eight)
• 9 (nine)

The decimal system uses positional notation to represent numbers larger than 9. This means that a digit's position in relation to other digits affects its meaning. Digits in the furthest right position represent the number of ones being counted, while digits in the second position from the right represent the number of tens. Digits in the third position from the right represent the number of hundreds, and digits in the fourth position from the right represent the number of thousands. This pattern can continue forever; for more information, see orders of magnitude.

For example, the number 535,254 means 5 hundreds of thousands, 3 tens of thousands, 5 thousands, 2 hundreds, 5 tens, and 4 ones. We would say this number as "five hundred thirty-five thousand two hundred fifty-four".

## The Basic Sets of Numerals

Counting numbers are the numbers we use every day to count things. Mathematicians sometimes refer to this set of numbers as the Natural Numbers. These are represented by the sign ${\displaystyle \mathbb {N} }$, for Natural Numbers.

${\displaystyle 1,2,3,4...\ }$

Whole numbers include all the counting numbers and zero.

${\displaystyle 0,1,2,3,4...\ }$

Negative numbers include the opposite of all the Counting Numbers. They are counted in the opposite direction of Counting numbers and have -, the negative sign, in front of them.

${\displaystyle ...-4,-3,-2,-1}$

Integers include all numbers without a decimal. Another way to say this is all of the Whole Numbers and their negatives. These are represented by the sign ${\displaystyle \mathbb {Z} }$, for the German word Zahlen, which means "numbers".

${\displaystyle ...-4,-3,-2,-1,0,1,2,3,4...}$