Is 1.1 rational or irrational

Answer 1

1.1 is the ratio of 11 to 10. It's rational. rational comes from the word ratio, so if the number can be expressed as a ratio of one whole number divided by another whole number than it is a rational number. 11/10 is a rational number. when trying to decide if a number is rational or irrational (like on a test), often its hard to know right away if the number could be expressed as a ratio of two whole numbers. so here is another clue. an irrational number can never be written out entirely. not only does the number go on forever, but it goes on forever with a sequence of numbers that never repeats. so if you can write the entire number (like 1.01, or 1.000000001) or if the number repeats, (like .33 or .1428) then it is rational. in fact, if the number is written with a decimal point than you know its rational. because they cannot be written out entirely, Irrational Numbers have to be expressed as a square root of another number, or one number raised to a fractional power (any power that is not a whole number)

all the rules summed up

1) number is a fraction (ei 1/3, 4/7, 16/2) - rational

2) number is written out (ei 1,2,3.0, 9.09, 1.00003) - rational

3) number is not completely written out but repeats (ei .33 or .1428) - rational

4) number is a square root of a square number (square numbers are 1,4,9,16,25,36,49, etc)- rational

5) number is a square root of a non-square number (non square numbers are all numbers except 1,4,9,16,25,36,49, etc)- irrational

6) number is rational number taken to a power that is a whole number - rational

7) number is any number taken to a power that is not a whole number - irrational

Answer 2

11 is rational. A rational number is one that can be expressed as the division of two integers. Since 11 is 11/1, among many other examples, it is rational.