2.2 Determine the exact for each of the calculations in 2.1 above, by working out the errors caused by rounding, and compensating for them. \( 2.2 .1723+586 \)

When adding numbers like \(2.1723\) and \(586\), rounding can introduce small errors. If \(2.1723\) is rounded to \(2.17\) (to two decimal places), you would be off by \(0.0023\). Thus, to find the exact sum, you compensate by adding this rounding error back into your total after performing the addition \(2.17 + 586 = 588.17\), and then consider the error \(588.17 + 0.0023 = 588.1723\). Another common mistake is forgetting to maintain appropriate decimal places in addition. Always align the numbers correctly by their decimal points to avoid losing precision. For example, performing \(2.1723 + 586\) directly yields \(588.1723\) without the rounding mishap. Remembering to include all significant figures is key to getting precise calculations!