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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 6.2 rational or irrational?
It is a rational number because it can be expressed as a fraction in the form of 62/1
Is 2.16 squared a irrational number?
No, (2.16) squared is not an irrational number. When you square (2.16), you get (2.16 \times 2.16 = 4.6656), which is a rational number since it can be expressed as a fraction (e.g., (46656/10000)). In general, the square of any rational number is also rational.
How do you show irrational number r uncountable?
To show that the set of irrational numbers is uncountable, you can use Cantor's diagonal argument. First, assume that the set of irrational numbers is countable and list them in a sequence. By constructing a new number that differs from each listed irrational number at a specific decimal place, you can demonstrate that this new number is also irrational and not in the original list, leading to a contradiction. Thus, the set of irrational numbers must be uncountable.
Is 2.20 percent rational or irrational?
It is rational number because 2.20% is the same as 0.022 which as a fraction in its lowest terms is 11/500 and only rational numbers can be expressed as fractions.
Is negative one half an irrational number?
No because -1/2 is a rational number expressed as a fraction
Is .22222222.a rational or irrational number?
If it ends there, it is rational. If it continues with the same digit (2 in this case) over and over, it is also rational.
Is an irrational number chosen at random is never a rational number?
An irrational number cannot be rational, so choosing at random is an irrelevance.
Is 0.777 an irrational number?
No it is not. It can be written as a fraction, so it cannot be irrational.
Is 0.3 a rational or irrational?
0.3 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
How can you tell the difference between a rational number and an integer?
You probably don't have to inspect that pair too closely.
Every integer IS a rational number.
What is difference between fractional and rational numbers?
All rational numbers are fractional but all fractional numbers are not rational.
For example, pi/2 is fractional but not rational.
What is an irrational number and examples?
An irrational number is a number that cannot be written as a ratio of two whole numbers. That is, there are no two integers, X and Y (with Y>0) such that the number can be written as X/Y.
Sqrt(2), pi, log(3) are examples of irrational numbers.
3 examples of irrational numbers?
3 examples of irrational numbers are:
- pi, which is approximately 3.14
- e or exponential, which is approximately 2.72
- the square root of 2, which is approximately 1.41
All values were given to three significant figures.
