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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
What is the easiest way to define rational numbers?
The set of fractions, such that both the numerator and the denominator are integers. Note that the integers themselves are included; you can write the integer 5, for example, as 5/1.
Is 81.57 a rational or irrational number?
81.57 is a rational number because it can be expressed as a fraction
Is the product of an irrational number and a rational number always an irrational number?
Not if the rational number is zero. In all other cases, the product is irrational.
What does a rational number times an irrational number equal?
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Is 3.1415926535897932384626433 a rational or irrational number?
Yes, that given terminating decimal is; however Pi is not.
3.1415926535897932384626433 can be expressed in the form a/b where a and b are integers and b is not equal to 0.
Give 5 examples of irrational numbers?
Irrational numbers are those that cannot be represented by a simple fraction, whereby the digits after the decimal point are neither repeating or terminating.
For example:
The value of pi:3.1415926535897932384626433832795....
The square root of 2 (√2):1.4142135623730950488016887242096....
The square root of 3 (√3):1.7320508075688772935274463415059....
The square root of 5 (√5):2.2360679774997896964091736687313....
The square root of 6 (√6):
2.4494897427831780981972840747059....
Is the square of pi a rational or irrational number?
The square of pi is an irrational number because it can't be expressed as a fraction.
What is the word i in the math problem 6i plus i?
i is the constant for the imaginary unit.
i ^2 = -1
and therefore i = squareroot of -1
What is the number for real gold?
If gold is real it will be stamped with a fineness number of 1-999 or .1-.999. It can also be stamped with a karat number of 10K, 14K, 18K, 22K or 24K.
Is the sum of two or more rational numbers is it rational or irrational?
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
If a number is a real number then is it also an irrational number?
No. All irrational numbers are real, not all real numbers are irrational.
Is -0.45 rational or irrational?
-0.45 is a rational number as a rational number is a number which can be written in fractional form or p\q form.So -0.45 can be written as -45\100.Hence,-0.45 is a rational number
Are there more rational numbers then irrational?
No. Although the count of either kind of number is infinite, the cardinality of irrational numbers is an order of infinity greater than for the set of rational numbers.
Is the square root of 26 rational or irrational number?
It is an irrational number because it can't be expressed as a fraction
Yes because the square root of 4 is 2 which is a rational and also a prime number
Is an integer a rational or irrational number?
Rational
The set of integers is a subset of the set of rational numbers. A rational number can be expressed as the ratio, or fraction of two integers a/b. So 1/2, 2/3, 5/6, 22/7, are all rational numbers. Also 3/1, -5/1, 20/5 are rational numbers, which are also integers.
