Question 892211: √51, -55, and -2/15. I need to know which classification of numbvers each are in. Please help!☺
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! To begin with,
 ,  and 
are all real numbers, but maybe you have not been introduced to any other kind of number, so I do not know if "real" is part of the expected answer.
Other than real, I can call those numbers other names:
is an irrational number (it cannot be expressed as a fraction, so it is not a rational number)
is a rational number (it can be expressed as a fraction),
is a rational number and can also be called an integer.
NOTES:
1) I do not know if you are expected to say that is positive, and that and are negative.
It seems too obvious, but maybe you are also expected to state the obvious.
2) Beware of tricks. You may be asked is  is rational, and you may be tempted to say it is irrational because of the square root sign. However,  so it is not irrational. You can call it a rational number, an integer, a whole number, and a natural number.
You could also be asked if  is a natural number. SInce  it is a natural number. It can also be called a whole number, an integer, and a rational number.
EXPLANATIONS:
The real numbers can be classified as rational numbers, or irrational numbers.
RATIOnal numbers show RATIOs of the simpler numbers we call integers. For example,  ,  and  are rational numbers. Rational numbers can also be written as decimals, such as  or  . (If the decimal has infinite digits, at least there is a repeating pattern, so you can write the exact value as a decimal by showing the repeated pattern followed by dots.
If a real number is not rational, it is called irrational.  and  are irrational. Their exact value cannot be written as a fraction or as a decimal. We end up using approximate values, like  or  for . People have calculated many digits of , and you could memorize the first few digits, but there is no pattern.
Some rational numbers can also be called integers, like  ,  , and  .
Some integers can also be called whole numbers (0, 1, 2, 3, ...).
Whole numbers other than can also be called natural numbers.
They first real numbers you ever knew were the ones we call "natural" numbers: 1, 2, 3, ....
They come to us very naturally, so it made sense to call them natural numbers.
The concept of zero is not so natural, but they teach you that early in school.
After that they teach you fractions, and they tell you that 0, 1, 2, 3, and so on are "whole" numbers, to differentiate them from fractions.
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