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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
Is -45.79348 rational or irrational?
It is rational because it can be expressed as a negative fraction
Is every irrational number a real number and how?
The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.
Irrational numbers between 2 and 2.5?
There are infinitely many of them.
They include
square root of (4.41)
square root of (4.42)
square root of (4.43)
square root of (4.44)
square root of (4.45)
square root of (5.3)
square root of (5.762)
square root of (6)
square root of (6.1)
square root of (6.2)
-3 is the ratio of -3 to 1. It's also the ratio of 3 to -1, and the ratio of -12 to 4, etc.
Any one of those facts proves that -3 is rational.
How do you find an irrational no between 0.365789 and 0.365478?
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.
What is the name for all sets of numbers?
There is a hierarchy of sets:
- Counting numbers
- Natural numbers (N)
- Integers (Z)
- Rational numbers (Q)
- Real numbers (R)
- Complex numbers (C)
- Quaternions, and possibly more.
What is a counterexample to the set of negative numbers is closed under subtraction?
-2 - (-5) = -2 + +5 = +3. (+3 is not in the set of negative numbers.)
Is 5.44 a rational or irrational number?
5.44 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be written as 544/100, which simplifies to 137/25. Since it can be represented in this way, it is considered rational.
What are the characteristics of a complex number?
A complex number must have a real and imaginary part.
It can be in the form: a + bi
i is an imaginary number and a and b are real numbers
What is the role of rational and irrational number plays in modern day calculation?
Rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions such as the square root of 2
Is 5.82147 is a rational or irrational?
it is rational, it can be written as a fraction: 582147/100000
irrational numbers CANNOT be written as a fraction
How do you find out if a decimal is rational?
If a decimal can be expressed as a fraction then it is a rational number
as for example 0.75 = 3/4
Also, if the decimal ever ends, or is a never ending repeat of the same digit
or group of them, then it's a rational number.
