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Q: Why can't repeating decimals be a rational number?

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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

first you think that is 2 a repeating decimal.... and can u reduce it if its not a repeating decimal and u cant reduce it then it is a rational number

rational decimals can be converted to a fraction example 0.2 irrational numbers cant be converted to a decimal like pi and √2

you cant get it

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

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, rational numbers are numbers that can be formed as a fraction hence -5/1 even with a minus sign on it irrational numbers are surd numbers, numbers that cant be expressed as a fraction

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.

Prime factorization refers to integers, not decimals.

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 decimal number is eitherterminating,repeating, ornon-terminating and non-repeating.The last of these can never be written out since it has infinitely many digits with no way of abbreviating them. A terminating decimal number is one with at most n digits after the decimal point (where n is finite). Such a number is equivalent to a rational number whose denominator is 10^n. The number is therefore rational.For example, 0.23568 = 23568/100000. It can be simplified but that is not relevant here.A number with a decimal representation with a recurring string of length m (where m is finite) is a rational number whose denominator is a 10^k multiple of 10^m-1 or 99...9 (m times). Here k is related to when the repeating sequence starts.For example, consider 1.23142857142857... (with the 6 digit sequence 142857 repeating)Let f = 1.23142857142857...then 100f = 123.142857142857...and 100f*1000000 = 123142857.142857142857...So that 999999*100f = 123142857-123 which is an integer.f is, therefore a ratio of two integers and so is a rational number.So that only leaves the irrational numbers for infinitely long decimal representations with no recurrence.

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