1.8 The test of reasonableness
Applying a test of reasonableness to an answer means making sure the answer makes sense. This is especially important when using a calculator as it is surprisingly easy to press the wrong key.
An example of a test of reasonableness is if you use a calculator to add 36 to 44 and arrive at 110 as an answer. You should know immediately that there is a mistake somewhere as two numbers under 50 can never total more than 100.
When using a calculator it is always a good idea to perform a quick estimate of the answer you expect. One way of doing this is to round off numbers. For instance if you are adding 1,873 to 3,982 you could round these numbers to 2,000 and 4,000 so the answer you should expect from your calculator should be in the region of 6,000.
Test your ability to perform the test of reasonableness by completing the following short multiple choice quiz. Do not calculate the answer, either mentally or by using an electronic calculator, but try to develop a rough estimate for what the answer should be. Then determine from the choices presented to you which makes the most sense, i.e., the choices that are most reasonable.
Activity 10
Choose the correct answer purely on what appears to be most reasonable.
| (1) 126 / 7= | (2) 17 x 26 = | (3) 6,460 / 760 = |
|---|---|---|
| a. 180 | a. 44.2 | a. 850 |
| b. 0.18 | b. 442 | b. 0.85 |
| c. 18 | c. 4,420 | c. 8.5 |
| d. 1.8 | d. 44,420 | d. 85 |
| (4) 330 x 8.4= | (5) 269 + 378= | (6) 562 – 268 = |
| a. 277.2 | a. 547 | a. 194 |
| b. 2,772 | b. 747 | b. 294 |
| c. 27,772 | c. 647 | c. 394 |
Answer
(1) c. 18
(2) b. 442
(3) c. 8.5
(4) b. 2,772
(5) c. 647
(6) b. 294