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By definition, an irrational number is a number that is not rational, or in other words a number that cannot be expressed as an integer divided by another integer. A number cannot be both "rational" and "not rational."

Q: Why can't numbers be both rational and irrational?

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But irrational numbers are decimals that can't be expressed as fractions

Well, for example, the square root of 4 is 2, which is a rational number. As long as the number which is being square rooted is not a square number itself (i.e. 1, 4, 9, 16 etc.), then it will be irrational. So..... the square roots of 49, 100, 196, for example, are all rational numbers (7, 10 and 14 respectively.) They do not have to be integers. The square of of any rational number automatically has a rational square root eg the square root of 77.41792 is 77.4179 . Rational means expressable as a ratio of integers: 77.4179 is 774179/10000 .

A mathematical approach:Yes they are. Irrational numbers are very real, for example - the square root of two - which is irrational (but can be plotted in a number line without difficulty with a compass and straight edge). All numbers you can think of (even if you cant white them out) are real numbers.They are real, but they can't be expressed as fractions.A philosophical approach:According to ME, there should be a limit. If there is a number which is not ending, we can't say that it is a number because it has not ended yet, its not a complete number. That's why, any number which is not ending is not a number, so irrational numbers and some rational numbers are not numbers and we can't plot them on real line, no matter how much depth we are into it. If there is a number 1.0000... (100 million 0's) ...1, we can plot it by dividing real line into required many parts but we cant plot a number like 1.1111....1111....(up to, we don't know), actually that's not a number yet.Maths should be changed.

it's Q Bar. i cant find a symbol for it on the keyboard. but its basically like The rational Symbol (Q) with a horzontal line on top of it.

3 and 5 are co-prime. So every integer can be expressed as a linear combination of 3 and 5. For example, 17 = (-1)*3 + 4*5 Since any integer can, any rational number can. That leave irrationals, which cannot.

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No irrational numbers don't have patterns and cant be expressed as a ratio so you cant even subtract the number. Ex: 22/7 - sqrt(2), you wont be able to find the difference since you cant even put it in a complete number.

No they cant because that would be contradicting each other ( The numbers wont end and don't have a pattern but rational is the complete opposite)

Yes.-5 is a rational number. It's the ratio of 5 to -1 .

This number is rational as 0.151155111555 = 151155111555 / 1000000000000 = 151291 / 1000899 if 0.151155111555 is the beginning of the number 0.151155111555111155551111155555.... then it's irrational as the decimals are not repeating and the sequence is infinite

But irrational numbers are decimals that can't be expressed as fractions

A decimal is rational if it:either ends and doesn't go on forever; ORit is a repeating decimal.A decimal is irrational if it goes on forever and ever and never stops without repeating.The number: 5.77777777 is rational because it goes on forever, REPEATING the same number (the digit 7).It can also repeat a group of numbers, like the number: 8.789789789789789789See how the "789" is REPEATING over and over again and never stops? That is a rational decimal!

there are so many irational numbers so it cant be placed on a list. This is like counting numbers, there are infinitive solutions! But you can clasify irational numbers. Irrational numbers normally are one number that has two rational numbers divided each other to get a number. to start this you will need some knowledge or examples or irrational examples. some examples are √3, √2, √5, √6, √7,√8,√10,√11,√12,√13,√14,√15,√17,√18,√19 ect, Also another example is π because there arent two rational numbers that multiply or divide to get the number. hope this hellped.

All irrational numbers are non-terminating decimals that can't be expressed as fractions

Well, for example, the square root of 4 is 2, which is a rational number. As long as the number which is being square rooted is not a square number itself (i.e. 1, 4, 9, 16 etc.), then it will be irrational. So..... the square roots of 49, 100, 196, for example, are all rational numbers (7, 10 and 14 respectively.) They do not have to be integers. The square of of any rational number automatically has a rational square root eg the square root of 77.41792 is 77.4179 . Rational means expressable as a ratio of integers: 77.4179 is 774179/10000 .

it's Q Bar. i cant find a symbol for it on the keyboard. but its basically like The rational Symbol (Q) with a horzontal line on top of it.

A mathematical approach:Yes they are. Irrational numbers are very real, for example - the square root of two - which is irrational (but can be plotted in a number line without difficulty with a compass and straight edge). All numbers you can think of (even if you cant white them out) are real numbers.They are real, but they can't be expressed as fractions.A philosophical approach:According to ME, there should be a limit. If there is a number which is not ending, we can't say that it is a number because it has not ended yet, its not a complete number. That's why, any number which is not ending is not a number, so irrational numbers and some rational numbers are not numbers and we can't plot them on real line, no matter how much depth we are into it. If there is a number 1.0000... (100 million 0's) ...1, we can plot it by dividing real line into required many parts but we cant plot a number like 1.1111....1111....(up to, we don't know), actually that's not a number yet.Maths should be changed.

irrational means something that cant make a fraction !!1