can some explain rational and irrational numbers for me?

Question

i dont have a good math teacher haha, hm, is zero rational?

Answer 1

Yes, zero is rational.

All rational numbers can be expressed as fractions. 0.75 is rational because it can be written as 3/4. 0.888888888..... is rational because it can be written as 8/9.

Irrational numbers cannot be expressed as fractions. Their decimal representations never repeat. Examples of of irrational numbers are √2 = 1.4142135623730950488016887242097... or pi = 3.14159265...

Tried to think of a good joke about this, but alas, nothing came to mind.

Answer 2

A rational number is a number that can be expressed in the form m/n, where m and n are both integers and n is non-zero. Since all the whole numbers (1, 2, 3, 4, 5) can be expressed as 1/1, 2/1, 3/1, 4/1, 5/1, it follows that all whole numbers are rational (including negative whole numbers). Also, any fraction with positive and negative whole numbers as numerator and denominator are rational numbers as well.

Rational numbers have the property that, in decimal form, they either terminate or repeat. If you punch in 1/3 in your calculator, you'll get 0.33333...(repeating forever). This is a sign of the rational numbers. If you get 1/7, you'll get a value which would repeat as well. 1/4 terminates into 0.25, but you can look at this as a non-terminating decimal as well, because in reality, we really have 0.25000000000000...(repeating forever).

An irrational number is one that CANNOT be expressed in the form a/b (for integers a,b). Similarly, in decimal form, they carry the property that their digits do NOT terminate NOR repeat. One of the more popular irrational numbers is PI. You'll encounter others in your final years of high school (sqrt(2), e, the various logs of numbers, etc).

To answer your question, 0 is rational because 0 can be expressed as 0/1, and as you can see, 0 is an integer and 1 is an integer.

Answer 3

In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero.

Each rational number can be written in infinitely many forms, for example 3 / 6 = 2 / 4 = 1 / 2, but the simplest form is when a and b have no common divisors. Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A fraction in this simplest form is said to be an irreducible fraction, or a fraction in reduced form.

The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part). The same is true for any other integral base above one, and is also true when rational numbers are considered to be p-adic numbers rather than real numbers. Conversely, if the expansion of a number for one base is periodic, it is periodic for all bases and the number is rational.

A real number that is not a rational number is called an irrational number.

In mathematics, an irrational number is any real number that is not a rational number, i.e., is not of the form n/m, where n and m are integers.

Almost all real numbers are irrational, in a sense which is defined more precisely below.

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common. A measure of a line segment I in this sense is a line segment J that "measures" I in the sense that some whole number of copies of J laid end-to-end occupy the same length as I.

Zero is rational

Answer 4

fractions are a part of a whole no. with positive sign. eg:1/7
rational no. are fractions with negative or positive signs. eg: -1/2, 3/6, -7/1, 4/-5. in other words, the definition of rational no. is:-
a no. of the form p/q where p is any integer and q is not equal to 0 is called a rational no.
since 0 = 0/1
and through the definition 0=p and 1=q
it has been mentioned that p is any integer, and q is not equal to 0,
since 0 is an integer 0/1 is a rational no. and so 0 is also a rational no.

Answer 5

Here is a easy way of thinking about this...

Rational: anything you can express with whole or fractional numbers. example: 1, 12, 1/3, .166666666 which is 1/6, etc, -22, -1/99.

Irrational: anything you can't express with whole or fractional numbers. example: square root of 2 which is 1.41421, pi which is 3.141562.......

and yes, zero is definitely a whole number 8)

Answer 6

rational numbers are those that can be expressed as the ratio of 2 integers. Examples include
1, 2, 2/3, 5/17etc there will be repeating digits
2/3=.66666.....
5/17=0.29411764705882352941176470588235
2941176470588235 keeps repeating
irrational numbers are those that cant be expressed as the ratio of 2 integer. examples include e, π, √2, √3
there is never a repeating pattern

Answer 7

zero is neither rational or irrational. rational numbers are numbers which can be expressed as a fraction.
irrational numbers are numbers that cannot be expressed as a fraction

Answer 8

rational nos are of the type p/q where q is non zero and p and q are integers
irrational numbershave non repeating non terminating decimals like 109.0100100001000001000000111100000111101...........

Answer 9

Yes zero is rational.
a few examples of irational numbers are
3/0
5/0
0/0
22/7
a few examples of rational numbers are
3
3/2
6/7
0/2