为什么 pi 不是有理数？

数系包括不同类型的数，例如质数、奇数、偶数、有理数、整数等。这些数可以相应地以数字和文字的形式表示。例如，40、65等以数字形式表示的数字，也可以写成40、65。

A Number system or numeral system is defined as elementary system to express numbers and figures. It is the unique way of representation of numbers in arithmetic and algebraic structure.

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数字用于各种算术值，适用于执行各种算术运算，如加法、减法、乘法等，这些运算适用于日常生活中的计算目的。数字的值由数字、它在数字中的位置值以及数字系统的基数决定。

Numbers generally are also known as numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities.

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数字是用于测量或计算数量的数学值或数字。它用数字表示为 2、4、7 等。数字的一些例子是整数、整数、自然数、有理数和无理数等。

数字类型

有不同类型的数字被实数系统分类为集合。类型描述如下：

自然数：自然数是从 1 到无穷大的正数。自然数的集合用' N '表示。这是我们通常用于计数的数字。自然数集可以表示为 N = 1, 2, 3, 4, 5, 6, 7,…
整数：整数是包括零在内的正数，从 0 计数到无穷大。整数不包括分数或小数。整数集由“ W ”表示。该集合可以表示为 W = 0, 1, 2, 3, 4, 5,…
整数：整数是一组数字，包括所有正数、零以及从负无穷到正无穷的所有负数。该集合不包括分数和小数。整数集由“ Z ”表示。整数集可以表示为 Z = .....,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...
十进制数：任何由小数点组成的数值都是十进制数。可表示为 2.5、0.567 等。
实数：实数是不包含任何虚值的集合数。它包括所有正整数、负整数、分数和十进制值。一般用“ R ”表示。
复数：复数是一组包含虚数的数字。它可以表示为 a+bi，其中“a”和“b”是实数。它用' C '表示。
有理数：有理数是可以表示为两个整数之比的数。它包括所有整数，可以用分数或小数表示。它用“ Q ”表示。
无理数：无理数是不能用分数或整数比表示的数字。它可以写成小数，小数点后有无穷无尽的不重复数字。它用' P '表示。

为什么 pi 不是有理数？

回答：

Pi(π): It is the ratio of the circumference of a circle to its diameter and is approx equal to 3.14159. If you divide the circumference of circle (is the total distance around the circle) by the diameter, will get exactly the same number doesnot matter the circle is big or small, the values of pi remains the same.

It is represented by the symbol π. The value Pi (or π) is mainly expressed in two different ways which are: Decimal or fraction: 3.14159…. or 22/7. Here it shows non terminating and non recurring digits.

Rational numbers are of the form p/q, where p and q are integers and q ≠ 0. Because of the underlying structure of numbers, p/q form, most individuals find it difficult to distinguish between fractions and rational numbers. When a rational number is divided, the output is in decimal form, which can be either ending or repeating. 3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1.

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.

Here, the given number, pi cannot be expressed in the form of p/q, because it’s a non terminating as well as non recurring decimal value.

Hence, π is an irrational number.

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