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.