Math and Numbers
The "abacus" was an early tool used for counting and some
simple mathematical operations.
Essentially, the reason Math came to being is that there was a need for counting things and for quantifying or determining how much of something was needed. Since human beings have 10 fingers it was only logical that the simplest way of counting was by using ten numbers: 1, 2, 3, 5, 6, 7, 8, 9 and 10. Using the same number system the reference to 5 pounds or 8 pounds of meat tells how much meat there is (This is how math is used for quantifying things).
The Number System can also be understood as numbers on an axis as shown on the figure below.
A vertical line indicates where the 0 point is and moving to the right is counting one more number.
The number axis is a graphical way to identify numbers.
The 3 dots after the number 4 indicate that there is no limit to how many numbers can be counted.
How about going to the left of the 0 line? It seems that there are negative numbers!
Well, yes going to the left of 0 starts counting -1, -2, -3, -4 and so on. Negative numbers are used to represent an opposite direction (such as going West instead of East) or a decrease from the "0 level",
such as -10˚ Farenheit.
If we were to zoom in to the positive part of the
axis, we would find out that there is quite a bit of space in between numbers 0
and 1 as well as in between 1 and 2 and each successive pair of numbers.
An expanded view of the number axis.
By dividing the space between 1 and 2 into 10 different equal segments we would create numbers in between the numbers 1 and 2. These numbers are given as: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, and 1.9. They are called fractional numbers, as opposed to whole (or entire) numbers such as 1, 2, 3 and so on. The number 1.5 is a fractional number lying halfway in between 1 and 2.
We could zoom in again and expand the axis and we would find out that there is also numbers in between the numbers 1.1 and 1.2. The digits to be used after the decimal point depend on how precise of a measurement is needed, and they all indicate fractional numbers.
Fractional numbers can we written in decimal form with numbers after the decimal point, or they can be written as fractions. Fractions is our next subject.