Irrational and rational numbers?

Question

It's my first time substituting in a middle school and I'm not very clear on what irrational and rational numbers are. And what is a rational number in equivalent form? Could somebody please explain this clearly, I don't want to disappointed the students.

Answer 1

A rational number is one that can be written as a fraction
or a terminating or repeating decimal. All integers are rational
numbers because they can be written with
denominator 1.
Examples of rational numbers: 3, 3.14, 22/7,
3.1415914159...
An irrational number cannot be written as a
terminating or repeating decimal.
Some examples:
√2, π, e, 1.010010001...
Equivalent fractions: a/b and ad/bd (d <>0, and d an integer)
are called equivalent fractions.

Good luck with the kids. Just explain everything
clearly and give lots of examples.

Answer 2

Yikes, we even have teachers consulting this forum? Crap, I'm glad I went to private school.

A rational number is a number that can be written in the form of a / b, where a and b are integers. Fractions are rational numbers if they're using integers in the top and bottom. Integers are rational numbers too, because for example you can always write 5 as the fraction 5/1. A real number that isn't rational is irrational.

An equivalent way of defining rational numbers is a number whose decimal terminates or repeats. 1/3 is "0.3333...." which has the 3s repeating. 1/4 is "0.25" which terminates. Something like √2 or π though doesn't terminate nor repeat anywhere in decimal form, so these numbers are irrational.

Answer 3

im not sure on this but i think a irrational number is when u have lets say 2/sqrt2 you tend to keep the denominator free of square roots so u mulitply by 1 so 1 = sqrt2/sqrt2

sqrt2/sqrt2 * 2/sqrt2 = 2sqrt2/2

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic. Every transcendental number is irrational.

The most famous irrational number is sqrt(2), sometimes called Pythagoras's constant. Legend has it that the Pythagorean philosopher Hippasus used geometric methods to demonstrate the irrationality of sqrt(2) while at sea and, upon notifying his comrades of his great discovery, was immediately thrown overboard by the fanatic Pythagoreans. Other examples include sqrt(3), e, pi, etc. The Erdos-Borwein constant

Answer 4

355/113 will recur with a era of length below 113. The definition wins right here and says that 355/113 is rational. the situation is in assuming that 355/113, which superficially imitates pi partly of its decimal illustration, would not terminate. yet another situation is interior the actuality that the rationals and irrationals are disjoint instruments via their definitions. i'm curious as to why you thought that 355/113 would not recur?

Answer 5

Irrational numbers are those which can not be put into p/q form, where p and q are integers.
ex : sqrt(2), pi etc
All the numbers excluding irrational are rational numbers