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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
0.123333 is this rational number,irrational number?
Oh, dude, 0.123333 is a rational number because it can be expressed as a fraction, like 12333/100000. Irrational numbers are like those mysterious, never-ending decimals that never repeat, you know, like pi or the number of times I've procrastinated doing my laundry. So yeah, 0.123333 is just a chill rational number, no biggie.
Which 2 consecutive whole numbers does the square root of 138 lie?
The square root of 138 is approximately 11.747. So, the two consecutive whole numbers between which the square root of 138 lies are 11 and 12. This is because 11^2 is 121, which is less than 138, and 12^2 is 144, which is greater than 138.
No, 6 over 5 is not irrational. Irrational numbers cannot be expressed as a ratio of two integers. In this case, 6 over 5 simplifies to the rational number 1.2, which can be expressed as a ratio of 6 to 5.
Well, isn't that a happy little question! Yes, 0.7171 is indeed a rational number, because it can be expressed as a fraction where the numerator and denominator are both integers. Just like painting a beautiful landscape, understanding numbers can bring a sense of peace and joy to your day.
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?
Since it is the square root of a negative number, it is actually imaginary, neither rational nor irrational. It is equal to 9i, or 9 times whatever the square root of negative one is.
square root of -81 = square root of 81 times i = 9i
What are the application of irrational numbers?
Real numbers which cannot be written in (a/b) form are called as irrational numbers like √3, √5,√2 etc. Now, we discuss applications of irrational numbers:
1. Use of pi(π) : pi is an irrational number which is use in many purpose in math like:
Area of circle = π * r2 where pi (π) = 3.14 and r is a radius.
Circumference of circle = π * d where d is a diameter of circle,
2. Use of exponential (e): e is an irrational number which is used in many parts of math-.
3. Use of cube root: cube root is basically used to find out area and perimeter of cube and cuboids because both have three dimension structures.
4. Use of irrational number to find out domain: irrational numbers are use to find out domain of particular function. For instance, domain of a function lies between 2 and 3 then we can represent them as √5. Similarly when domain lie between 1 and 2 then we represent them as √2 and between 3 and 4, we can represent them as √11 etc.
So, irrational numbers are used in finding approx value of any real measurement because it is difficult to find out exact value of real measurement. Irrational numbers are calculating non terminating point of function.
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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?
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
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, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)
