Page 1

Is 2 A Rational Number Is 2 A Rational Number

We know that Rational Numbers are the numbers written in form of a/b where a and b are integers and b≠0. Also, 2 can be written as 2/1. On comparing we get a=2 and b=1, So, both a and b are integers and b≠0. The answer for the query that is 2 a rational number is yes, 2 is a Rational Number. In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold , Unicode ℚ), which stands for quotient. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Know More About Rational Numbers Properties

Tutorcircle.com

Page No. : ­ 1/4


The rational numbers can be formally defined as the equivalence classes of the quotient set (Z × (Z ∖ {0})) / ~, where the cartesian product Z × (Z ∖ {0}) is the set of all ordered pairs (m,n) where m and n are integers, n is not zero (n ≠ 0), and "~" is the equivalence relation defined by (m1,n1) ~ (m2,n2) if, and only if, m1n2 − m2n1 = 0. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational. The definition of "rational number" is: "Any number that can be written as the ratio of two integers." '2' can be written as 2/1, 4/2, 6/3, 8/4, 792/396, and a lot of other ratios of integers. It satisfies the definition of "rational number". That makes it a rational number. The answer given up above the broken line doesn't do it. It's true that the decimal form of an irrational number never ends, but that fact can't be used as a definition, because it doesn't work the other way. A decimal that never ends is not necessarily an irrational number. 0.333333333... never-ending is the decimal representation of 1/3, which is a perfectly good rational number. Read  More About Rational Expressions Calculator

Tutorcircle.com

Page No. : ­ 2/4


A rational number has a decimal that is either terminating or repeating. 2/3 is rational because it's equal to 0.6666 repeating. It repeats, therefore is rational. 1/7 = 0.142857 repeating, therefore is rational. 1/2 is rational because it is equal to 0.5. The decimal is terminating. An irrational number is non-terminating and does not repeat any pattern. Pi is irrational because it is equal to 3.14159 and goes on for a large number of digits. Therefore it's irrational.

Tutorcircle.com

Page No. : ­ 2/3 Page No. : ­ 3/4


Thank You

TutorCircle.com

Is 2 A Rational Number  

The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold , Unicode ), which stands for quotient. ℚ We know tha...

Read more
Read more
Similar to
Popular now
Just for you