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What is the decimal expansion of an irrational number?
A decimal expansion means to write out the base 10 digits of a number. Because irrational numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion: 3.14159265... Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if there were a finite number of digits, you could express it as a fraction, which would not be irrational.
Is 7.11 rational or irrational?
A number with a finite number of decimal digits is always rational. (If the number of decimal digits is infinite, the number is rational only if there is a repeating pattern.)
Is the sum of a rational number and an irrational number always irrational?
Yes, always.
Is the sum of an irrational number and rational always irrational?
Yes.
Is the product of a rational number and an irrational number always irrational?
No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.
