Question

Integers are _____ irrational numbers.

always
sometimes
never

Answer 1

Integers are $never$ irrational numbers.

Answer 2

Answer-

Integers are never irrational numbers.

Explanation-

Integers -

Integers are set of real numbers consisting of the natural numbers, their additive inverses, and zero.

The set of integers is usually abbreviated J or Z.

Moreover, the sum, product, and difference of any two integers is an integer. But this cannot apply to division.

Rational numbers -

Rational numbers are those numbers that can be expressed as a ratio between two whole numbers. as an example, the fractions 13 and -11118 are both rational numbers. All integers are included in the rational numbers because any integer z can be written because the ratio z1.

All decimal places that end are rational numbers (because 8.27 is written as 827100.) Decimal numbers that have a repeating pattern after a certain point are rational: e.g.

0.0833333....=112.

The set of rational numbers is closed under all four basic operations, that is, given any two rational numbers, their sum, difference, product, and quotient are additionally real (unless we divide by 0).

Irrational numbers

A real number can be a number that cannot be written as a quotient (or fraction). In decimal form, it never ends or repeats. the traditional Greeks discovered that not all numbers are rational; there are equations that cannot be solved using integer ratios.

The first such equation to be studied was 2=x². How many times is itself equal to 2? But you'll never get exactly right using the square of a fraction (or the trailing decimal). The root of two is real, meaning that its decimal equivalent lasts forever, with no repeating pattern:

√2=1.41421356237309...

Other famous irrational numbers are the golden ratio, a variety of great importance to biology:

1+5√2=1.61803398874989...

and e, the most important number in the number:

e=2.71828182845904...

Irrational numbers can be further divided into algebraic numbers, which are solutions to some polynomial equation (like 2√ and thus the golden ratio), and transcendental numbers, which are not solutions to any polynomial equation. π and e are both transcendental.

Therefore, Integers are never irrational numbers.

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