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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 are the irrational numbers?
Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.
Who invented the irrational number set?
Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
When was Irrational Number discovered and what was the dete?
Irrational numbers have been known since very early times. For example, it was recognised that the length of the diagonal of a unit square was not a rational number. There is, therefore, no specific date.
Is -2.2422422242222422224 rational or irrational?
Answer:
-2.2422422242222422224 is rational.
Rational numbers are numbers that can be expressed as the division of two integers, the divisor not being zero. -2.2422422242222422224 can be expressed as -22422422242222422224 divided by 10000000000000000000.
Answer:
If the number appears exactly as you wrote it in your question, then the number is rational as explained in the first answer.
However, I wonder if you might have left off the three dot "continuation symbol" and a "2". Irrational numbers cannot be properly expressed in decimal form (the decimal representation goes on forever without repeating), so sometimes we write the first few digits and put an ellipsis at the end to show they go on forever. Examples would be
pi = 3.14159...
e = 2.71828...
If you meant to write -2.24224222422224222224... then the number is (probably) meant to be irrational.
When were irrational numbers first used?
If you mean by 'used' when were they first discussed then that was probably the Pythagoreans of Greece around the 5th century BC. They didn't use them so much as argue about them!
The first mathematician to use them systematically was Abu Kamil Shuja ibn Aslam of Egypt, around the 9th century. He used them as solutions and coefficients of equations.
For more information please see the wikipedia article about irrational numbers.
Is. -1.23654 an irrational number?
No because it can be expressed as a fraction and so therefore it is a rational number
Is negative 12 fourths a real rational irrational whole natural and integer?
It is -3, which is an integer
What is 5 sentences about contrasting rational and irrational numbers?
rational and irrational numbers are two types of real Numbers. all real numbers which are terminating and non terminating but repeating comes in the category of rational numbers. all real numbers which are non terminating and non recurring comes in the category of irrational numbers. rational numbers are expressed in the p/q form where p and q are both integers and q is not equal to 0.the opposite the case is with irrational numbers. they are not expressed in the p/q form
How else can you get an irrational number?
"How else" in the question implies that you already have some methods that you have in mind. But you have chosen not to share that information. I cannot know whether a method that I suggest is one that you already know of, and therefore, regrettably, the question cannot be answered.
Is 15+0.07 rational or irrational?
The expression 15 + 0.07 is a rational number. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In this case, you can express 15 + 0.07 as 15.07, which is a rational number.
Is 27.5 rational or irrational?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.
