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Rational Numbers

Satisfactory Essays
College Mathematics
Mohave Community College
Kelsey Uhles
May 3, 2014

In math we must know how to classify different numbers. Numbers can be classified into groups which with a little bit of studying are easy to understand over time. Terms in math are thrown around easily and if you don’t understand the terms math will suddenly become much more difficult. The terms and groups that I am referring to are where the different numbers fall into different groups. These groups are Natural numbers, Whole numbers, Integers, Rational numbers, Real numbers, and Irrational numbers.
First Natural numbers which are what we use and see as our counting numbers. These numbers consist of these simple numbers 1, 2, 3, 4… and so on. Whole numbers are the next numbers which include all natural numbers along with the number zero which means that they are for example 0, 1, 2, 3, 4… and so on. Integers can also be whole numbers but also can be whole numbers with a negative sign in front of them. Integers are the individual numbers such as -4, -3, -2, -1, 0, 1, 2, 3, 4… and so on. Rational numbers include integers along with fractions, and decimals. Examples for Rational numbers include ¼, -¾, 7.82, 2, 123/25, 0.3333. Irrational numbers do not include integers or fractions. Although Irrational numbers are the only group that is classified with numbers that can have a decimal value that can continue for however long with no specific pattern unlike rational numbers. An example of an irrational number could be pi. Pi which we usually just round to 3.14 is actually 3.1415926535897932384626433832795… and this continues on for trillions of digits. And last comes Real numbers which include natural numbers, whole numbers, integers, rational number...

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...er is rational such as √2 , we can then go to the next step. Recalling that refers only to the positive square root of 2, this means that could be written as the quotient of two positive integers, such as √2 =a/b, where the fractions in lowest terms. We can assume that a and b have no common factors. We can then use simple algebra to find out the conclusion as the following:
√2b=a
(√2b)^2=a^2
2b^2=a^2
With this we are able to determine that a^2 is in fact an even number and that a^2 has 2 as a factor. Since a^2= axa it says that 2 must be a factor of a. Which says that a itself is an even number but that a^2 has 4 as a factor, and therefore 2b^2 has 4 as a factor. Then b^2 has 2 as a factor so that b^2 is an even number. So a/b would not be in its lowest terms since both a and b have 2 as a factor which shows that √2 is an irrational number and cannot be rational.
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