# What is the difference between a rational and irrational number and what is a rational and irrational number

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And also what is/makes a integer?

In: 0 An integer is a counting number (1, 2, 3, 4… and so on), zero, or the negative of a counting number (-1, -2, -3, -4, and so on). What I’m calling “counting numbers” here are more properly called *natural numbers* in math, but you may not be familiar with the term.

A rational number is a number that can be written as a fraction, where both the top and bottom values are integers. Put another way, a rational number can be gotten by dividing one integer by another. 1/2 is a rational number, but not an integer. 7 is both, since it’s both an integer and can be written as 7/1 (where both 7 and 1 are integers). All integers are rational numbers, but most rational numbers are not integers.

An irrational number is a (real) number that is not a rational number. The best known examples are pi and the square root of 2, neither of which is equal to any fraction with only integers in it. An integer is a whole number; 1, 42, 1,299,340 these are all integers.

A rational number is one that can be expressed as a fraction; 0.5=1/2, 0.75=3/4 etc.

An irrational number cannot be expressed as a fraction, for example pi has an infinite number of decimal places and so therefore cannot be expressed as a fraction. The integers: “whole numbers” ie 0, 1, 2, 3, 4…, but also -1, -2, -3, -4….

Rational numbers: fractions, numbers that can be represented as one integer divide by another. 1/2, -7/65, etc. Note that all integers are also rational (if you like you can say that eg 4 = 4/1 so that they look like the other rationals).

Irrationals: numbers that aren’t rational, like the square root of 2 or π.

That’s really all there is to it. It may be surprising that irrational numbers exist (Pythagoras had the person who proved that the square root of 2 was irrational murdered). Integers are just all the positive and negative (and zero) whole numbers. Anything that you can write without a decimal point is an integer.

The rational numbers are defined as any number you can make by dividing one integer by another. (Except for dividing by zero). They are things that can be written as a ratio, like 1/2 is rational, 420/69 is rational.

Irrational numbers are all those numbers that *cannot* be written that way. We know what some of them are because they have special properties, but the vast majority of them are completely unknown because we don’t have a good way of writing them. But examples include pi, sqrt(2), and the number e. Integers are the whole numbers you can count. Like -3, -2, -1, 0, 1, 2, 3.

Think of it as counting things without breaking them apart. Unless you have a broken chair, you probably have an integer of chairs in your home. Well, ok, maybe not a negative integer.

A rational number is a number that is a fraction/division of two integers. So 0.5 would be a rational number, that’s 1/2. One divided by two becomes 0.5

47.38281 and 575885.2 and 67.6767676767… are all also rational numbers because they can each be equated to the fraction of two integers.

Meanwhile, an irrational number is any number that can’t be written as a fraction of two integers.

The square root of 2, for example, is irrational. You can only approximate it by continous fractions. You’d have to do an infinite amount of fractions to describe the whole number.

Same with π, e and the golden ratio.

Their decimals go on forever.