We can prove that the square root of any prime number is irrational. So √2, √3, √5, √7, √11, √13, √17, √19 … are all irrational numbers.
0:162:56How to find irrational numbers between any two fractional numbers?YouTubeStart of suggested clipEnd of suggested clipSo all you have to do is divide. 1 by 7. We get 0.14 2 8 5 7 which is a recurring. And divide 2 by 7MoreSo all you have to do is divide. 1 by 7. We get 0.14 2 8 5 7 which is a recurring. And divide 2 by 7.
There are Infinite number of irrational numbers between two rational numbers.
Between any two numbers, however large or small the difference between them may be, we have infinite rational as well as irrational numbers. As such between 1 and 6 too we have infinite irrational numbers. Irrational numbers in their decimal form are non-repeating and non-terminating numbers.
infinite numberThere are an infinite number of irrational numbers between any two rational numbers.
There are infinite numbers of rational numbers between any two rational numbers. So the answer is infinite.
So, for example, 0.123123123123…, with 123 repeating forever, is rational (in fact, it is equal to 41/333), whereas something like 0.123456789101112131415…, which will never repeat, is irrational.
3 irrational numbersWe know that √2 = 1.414... and √3 = 1.732... Keeping the above conditions in mind, we find the 3 irrational numbers between √2 and √3. Note that we can have infinitely many irrational numbers between them.
3.1416 is a rational number because it is a terminating decimal.
41/333A repeating decimal is a decimal that does not terminate but keeps repeating the same pattern. For example, 0.123123123. . . is a repeating decimal, the “123” will repeat endlessly. Any repeating decimal is equal to a rational number. For example, 0.123123. . . is equal to 123/999, or 41/333.
Answer: The two rational numbers between 3 and 4 are 3.5 and 3.75. Two irrational numbers between 3 and 4 are √11 and √13.
The simplest exact fraction for the decimal number 0.123 is 1231000 .
Rational numbers have decimal expansions which repeat periodically. For example 0.123123 An irrational number like √2 has a decimal expansion which does not repeat: √2 = 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070
NOTE: Pi is an irrational number, the number 3.1416 is just a close approximation to Pi and it is rational.
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