## Irrational Approximations

An irrational number is a non-repeating, non-terminating decimal. It’s decimal representation, is an approximation of its value. Irrational numbers are rounded when written in decimal form.

We can take advantage of the square root key (√ ) on a calculator to find approximations for some irrational numbers.

Example: $$\sqrt{5}$$ = 2.236067977…….. Since it is impossible to write out the entire decimal (since it never ends) we may approximate $$\sqrt{5}$$ to be 2.2 or 2.24 or 2.236, etc., depending upon the rounding directions given in the problem.

If no specific rounding directions are given in a problem, work with the full calculator display, or work with the number in its original form (in this example, work with $$\sqrt{5}$$.)

Don’t round too soon! You should always work with the “full” value of a number (such as $$\sqrt{5}$$), or the full calculator display of the number, in a multi-step problem, saving the final rounding for the last step.

If using a calculator, work with the full calculator entries until you are ready to round your final answer.