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Why the product of nonzero rational number and an irrational number is an irrational?
Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.
Is the number 0.3333 is irrational?
This is a rational number because it terminates at the 4th 3. If it was 0.3 recurring then it would be irrational.
Why is the sum of an rational number and irrational number an irrational number?
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Can an irrational number become a rational number?
How would you do that ?? You'd have to change the value of the number. As long as the irrational number keeps its original value, it's an irrational number.
Is 2.8333333 a rational number or irrational number?
A rational number is any number that does not have an infinite number of digits. So, as you wrote it, 2.8333333 is a rational number. However, if you meant the 3s to go on forever (as in the number 2.8 + 1/30), that would be an irrational number.
