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It is not! The square root of 2, for example, is irrational but you can always locate it exactly by using the diagonal of a unit square.

Q: Why is the location of an irrational number an approximate location?

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Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.

An irrational number.

When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.

It is not an irrational number!

Yes, it will always be irrational.

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6.13579244 (approximate, this is an irrational number)

Simply plot the irrational number at it's approximate location on the number line and label the irrational number. For example, if you were to plot pi on the number line, you would plot it at about 3.14 and label it with "π" (the pi symbol, if it doesn't show up) Another example is if you want to plot the square root of 2 on the number line. You would plot it at around 1.414 and label it with "√2"

If the simplified form of an expression contains an irrational number and a numerical evaluation is required then it is necessary to use a rational approximation.

Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.

Approximate location of what, exactly?

An irrational number.

No. The sum of an irrational number and any other [real] number is irrational.

The sum of a rational and irrational number must be an irrational number.

No, 3.56 is not an irrational number. 3.56 is rational.

rational * irrational = irrational.

-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.

No. A number in 'decimal' format is either exact or approximate; there is no reduction needed or possible. A 'decimal' may be approximate if it is irrational (for example, pi, 3.14159...) or repeating (for example, 1/3, which is 0.333333....).