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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 the square root of 25 a rational number?
Yes, the square root of 25 is a rational number. A rational number is any number that can be expressed as a fraction of two integers. The square root of 25 is 5, which can be expressed as the fraction 5/1. Therefore, 5 is a rational number.
Is 0.757575 rational or irrational?
The number 0.757575 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 0.757575 can be expressed as the fraction 75/99, which meets the criteria for a rational number.
Rational!!!!
Consider ALL numbers to be rational , except those decimals that gor to infinity AND there is no regular order in the decimal digits.
Rational ; 2.33333..... Because the decimals are in a regular order.
Irrational ; 3.141592.... Because the decimals are in an irregular order.
The mathematical definition of irrational numbers that they cannot be converted to a quotient(fraction).
NB The three or more stops after the last decimal is the mathemtical indication that it recurs to inifinity. If no stops are shown, then it is deemed to be a terminal decimal.
e.g. 2.333 is a terminal decimal
2.33333..... is a decimal recurring to inifity.
NNB pi = 3.141592... is the most well known irrational number.
However, the 'Square Roots' of prime numbers are also irrational
e.g. sqrt(2) = 1.414213562....
sqrt(19) = 4.358898944....
What is an irrational number between 14.2 and 14.3?
Well, isn't that a happy little question? An example of an irrational number between 14.2 and 14.3 is the square root of 2, which is approximately 1.414. It's like a little mathematical friend that goes on forever without repeating, just like the beauty of nature around us.
Is 75.082106 repeating rational or irrational?
The number 75.082106 with a repeating decimal is rational. A rational number can be expressed as a fraction of two integers, where the denominator is not zero. In this case, the repeating decimal can be written as a fraction, making it a rational number. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
What numbers are less than -22?
Numbers less than -22 would be any number that falls to the left of -22 on the number line. This includes all negative numbers greater than -22, such as -23, -24, -25, and so on. It also includes all decimal numbers between -22 and 0, such as -22.5, -23.7, and so forth. In summary, any number less than -22 is considered to be in this set.
Is 1.7777777 a irrational number?
Well, honey, let me break it down for you. If you're talking about the decimal 1.7777777, then no, that's a rational number because it can be expressed as 8/9. But if you're referring to the infinite string of 7's, then yes, that's irrational because it can't be expressed as a simple fraction. So, it really depends on which 1.7777777 you're talking about, sugar.
NO!!
Irrational Numbers are those where the decimal digits go to infinity AND there is no regular order in the decimal digits.
pi = 3.141592.... is the most well known irrational number.
as are the 'Square roots' od prime numbers;-#
sqrt(2) = 1.414213....
sqrt(3) = 1.73205...
sqrt(5) = 2.23606...
However,
such as numbers as
3.3333..... is NOT irrational, because the decimals are in regular order.
Similarly
2.373737....
or
5 .678678678....
Are NOT irrational because the decimals are in a regular order.
NB '....''' at the end of a decimal is the mathematical indication of recurring to infinity.
Is 0.285714 rational or irrational?
Well, darling, 0.285714 is rational because it can be expressed as a fraction, specifically 2/7. Rational numbers are just numbers that can be written as a fraction, so this one fits the bill. But hey, don't worry about it too much, just keep being fabulous!
Is 6 a rational or irrational number?
Well, honey, 6 is about as rational as a person can get! It's a whole number, which means it can be expressed as a fraction (6/1), making it a rational number. So, yes, 6 is definitely a rational number, no ifs, ands, or buts about it!
Irrational number between 8 and 9?
An irrational number is a number which cannot be expressed as a fraction made of integers. These numbers generally have infinite decimals with no pattern to them whatsoever.
The easiest way, I think, to make an irrational number is to take the square root of a number between the squares of your parameters, in this case between 64 and 81. Thus a number such as square root(72), which is 8.485281..., or square root(80), which is 8.944571..., will do nicely.
Is the square root of -81 rational or irrational?
The square root of -81 is an imaginary number, specifically 9i, where i represents the imaginary unit equal to the square root of -1. Since the square root of -81 does not result in a real number, it is considered irrational. Rational numbers are those that can be expressed as a ratio of two integers, whereas irrational numbers cannot be expressed in this form.
What are the application of irrational numbers?
Oh honey, irrational numbers are used in all sorts of fun ways! From calculating the diagonal of a square to measuring the circumference of a circle, these quirky numbers pop up everywhere in math and science. So next time you come across a pesky square root or a never-ending decimal, just remember that irrational numbers are here to keep things interesting.
Is the square root of 11 rational or irrational?
The square root of 11 is irrational. An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. In the case of the square root of 11, it is a non-repeating, non-terminating decimal and cannot be simplified further. Therefore, it falls under the category of irrational numbers.
NO!!!!
Irrational numbers are thouse were the decimals go to inifinity AND there is no regular order in the decimal digits.
'pi' of circular fame is probebly the most well known irrational number at ;-
3.141592.....
NB Any terminating decimal e.g. 3.12 is NOT irrational.
Is 5 out of 13 rational or irrational?
5 out of 13 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are both integers, and the denominator is not zero. In this case, 5 can be expressed as the fraction 5/1, making it a rational number.
Is 0.727272 a rational number irrational number both irrational and rational or neither?
Oh honey, 0.727272 is a rational number. It can be written as 8/11, which is a nice, tidy fraction. So, it's not irrational, not both, and definitely not neither. Just a good ol' rational number, nothing fancy.
Which irrational number is closest to 6?
The irrational number closest to 6 is the square root of 36, which equals 6. This is because the square root of 36 is a rational number that is the closest approximation to 6 among irrational numbers. The square root of 36 is equal to 6, making it the irrational number closest to 6.
Is negative 35 an irrational number?
Oh, let's not worry about negativity, friend. Negative 35 is not an irrational number. Irrational numbers are those that cannot be expressed as a simple fraction, but negative 35 can be written as -35/1, making it a rational number. Just like every brushstroke adds beauty to a painting, every number has its place in the vast world of mathematics.
Is the set of all irrational number countable?
No, the set of all irrational numbers is not countable. Countable sets are those that can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). The set of irrational numbers is uncountable because it has a higher cardinality than the set of natural numbers. This was proven by Georg Cantor using his diagonalization argument.
Is 12 over 18 a rational or irrational number?
The fraction 12/18 can be simplified to 2/3 by dividing both the numerator and denominator by their greatest common divisor, which is 6. Since the fraction 2/3 can be expressed as a ratio of two integers and can be written in the form a/b where a and b are integers and b is not equal to 0, it is considered a rational number. Rational numbers are numbers that can be expressed as a ratio of two integers.
Oh, dude, you're hitting me with the math questions! But like, yeah, 0.025 is a rational number because it can be expressed as a fraction, like 25/100. Rational numbers are just numbers that can be written as a ratio of two integers, so 0.025 totally fits the bill.
Is 15.77 a rational or irrational number?
15.77 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 15.77 can be written as 1577/100, which meets the criteria for a rational number.
Is 5.123 rational or irrational?
The number 5.123 is rational. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 5.123 can be expressed as the fraction 5123/1000, where both the numerator (5123) and the denominator (1000) are integers.
