math help?

Question

i am in algebra and i have to classify numbers like -5 ,2 ,5/2
64 squared etc. i have to classify them as real,rational,irrational,integer,and whole numbers i dont understand how you know which number is which.

Answer 1

Real numbers
Counting numbers: 1- infinity
Whole numbers: 0-infinity
integers: - infinity - + infinity( negative and positive numbers)
rational: fractions, terminating decimals.
- - - - -
irrational: non perfect squares, never ending decimals ( pi, square root of 7)

Its a tree, so integers include whole numbers and rationals include integers. Irrational is separate from the others though. All fall under the category of real numbers.

Answer 2

There is an order to this, going from simpliest to more complex. The easiest numbers are the natural numbers. These are the counting digits, 1,2,3,4... and so on. Then come the integers. These are the natural numbers combined with the negative natural numbers, such as -3,-2,-1,0,1,2,3.. and so on in either direction. Then come the rational numbers. These are numbers that can be expressed as fractions, or the quocient of two integers. Examples include 1/2, 3/4, 99/100, 5777/8881. These are decimal numbers that end or repeat themselves. Then there are the irrational numbers. These are decimal numbers that never end and never repeat a string of digits. Some are very important in math. such as pi, which relates a circle's circumference and radius, which is 3.1415926..., and e (Euler's constant) that is important in many areas of math and science, and is 2.7182818... All these types of numbers (Natural,integer,rational and irrational) make up real numbers. Then come complex numbers, which have to do with taking the square root of a negative number.

The easiest way to think about this is to relate it to what you use every day. Almost everyone uses the integers every day to count and balance check books, to do simple math. Then come the rational numbers. Numbers that make sense to a person because people deal with fractions on a regular basis, such as in cooking and measurement. their rational, your mind can make sense of them. Then comes the irrational numbers. Numbers that continue on forever and are rarely used except for in math and science. these numbers are irrational, or hard for your mind to comprehend because they have no use for laymen.

Answer 3

Learn the definitions of these terms. Since mathematics is an abstract science (you can't touch it, you can't taste it, etc.), you must learn definitions. If not, you quite literally never know what you are talking about.

Consult your text (or your instructor) for appropriate definitions, and then memorize them just as you memorize definitions in English vocabulary.