Is 0 Rational Or Irrational
Is 0 Rational Or Irrational
Zero is several sorts of numbers. It is actually both. "Real numbers", "Rational numbers",
"irrational numbers", "integers", "trancendental numbers", "cardinal numbers" and so forth, all
have their own definitions. These definitions define a SET of numbers. A single number can
belong to several SETs.
Real numbers are numbers that can be written as an infinite decimal expansion. It includes
numbers like fractions eg 1/7 and PI. Real numbers can also be split into algebraic and
transcendental numbers but the definition is too complicated here. 0 is a member of this SET
Rational numbers work out to be the same but there is a slightly different definition. 0 is a
member of this SET.
Irrational numbers belong to the set of two dimensional numbers of the vector form a + b x i
where i is the square root of -1. 0 = 0 + 0 x i so zero is also a member of this SET
Integers are the set of normal counting numbers both positive, negative and 0.
A Rational number is one that CAN be expressed as the division of two Integers.
0/1 = 0
0/2 = 0
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0/N = 0 ; if N is an Integer different than zero.
So Zero IS a Rational Number.
Without taking away the truth of this, watch out for:
0/0 which is NOT 0. (some will say this value is Undefined, others will say it is Infinite)
Note that a Rational Number does not have to be an Integer.
i.e. 0.75 is a rational Number since it is 3 divided by 4 (i.e 3/4, or 6/8, etc.).
A Famous NON Rational Number is PI = 3.141592654......
PI is NOT Rational since there are no Integer numbers A and B that divided will yield PI.
A rational number is a number that can be written as a ratio. That means it can be written as a
fraction, in which both the numerator (the number on top) and the denominator (the number
on the bottom) are whole numbers.
The number 8 is a rational number because it can be written as the fraction 8/1.
Likewise, 3/4 is a rational number because it can be written as a fraction.
Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be
written as a fraction.
Every whole number is a rational number, because any whole number can be written as a
fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be
written as 3,867/1.
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All numbers that are not rational are considered irrational. An irrational number can be written
as a decimal, but not as a fraction.
An irrational number has endless non-repeating digits to the right of the decimal point. Here
are some irrational numbers:
π = 3.141592…
Although irrational numbers are not often used in daily life, they do exist on the number line. In
fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!
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