Math you can really use every day

weather and finance. But there's more.

RATIONAL NUMBERS

Look at any one of the preceding three number lines. What go between

those hash marks (also known as hache marks)? We remember from

geometry that a line segment is a continuous string of points. Shouldn't

there be values for the other points on that line, and not just the few

that we've marked? Indeed there are. In order to reach them we must

once more expand the realm, to now include rational numbers.

A rational number is any number that can be expressed as a frac-

tion, such as 1 /2, 1 /3, 3 /5, or 5 /8. Any integer can be written as a fraction.

For example, 6 is equal to 6 /1 or 12/2. A common fraction has two parts,

as illustrated below:

numerator

denominator

Consider a pizza pie that has been cut into eight equal slices, three

of which are still in the pan. The denominator tells us into how many

parts the whole has been cut. The numerator specifies how many of

those slices are being considered. So the number of slices of pizza

still in the pan compared to the original intact pie is represented by

the fraction 3 /8. The number of slices missing from the pan is repre-

sented by the fraction 5 /8. When the pie came out of the oven and

was first sliced, there were 8 /8, which is equivalent to one whole pie.

5 3

8 8

3 5 8

+ =

8 8 8

Not only is the realm of rational numbers infinite, but the number

of rational numbers that may exist between any two consecutive

whole numbers is also infinite. That is to say, there are an infinite num-

ber of fractions between 1 and 2, an infinite number of fractions

between 2 and 3, and so on.

8 Math You Can Really Use--Every Day

Any common fraction may also be expressed as a decimal or a per-

cent. Certain common fractions, when expressed as a decimal, form

repeating decimals, for instance 1 / 3 = 0.333333333 . . . ad infinitum.

Also, 1 /6 = 0.1666666666. . . . Repeating decimal fractions are consid-

ered to be part of the realm of rational numbers.

IRRATIONAL NUMBERS

Other fractions form decimals that do not follow a pattern of repeti-

tion. The fraction represented by the Greek letter pi = 22 / 7, which