Sanity Testing - Mathematical

Mathematical

A sanity test can refer to various orders of magnitude and other simple rule-of-thumb devices applied to cross-check mathematical calculations. For example:

• If one were to attempt to square 738 and calculated 53,874, a quick sanity check could show that this result cannot be true. Consider that 700 < 738, yet 700² = 7²×100² = 490000 > 53874. Since squaring positive numbers preserves their inequality, the result cannot be true, and so the calculated result is incorrect. The correct answer, 738² = 544,644, is more than 10 times higher than 53,874, and so the result had been off by an order of magnitude.
• In multiplication, 918 × 155 is not 142135 since 918 is divisible by three but 142135 is not (digits add up to 16, not a multiple of three). Also, the product must end in the same digit as the product of end-digits 8×5=40, but 142135 does not end in "0" like "40", while the correct answer does: 918×155=142290. An even quicker check is that the product of even and odd numbers is even, whereas 142135 is odd.
• When talking about quantities in physics, the power output of a car cannot be 700 kJ since that is a unit of energy, not power (energy per unit time). See dimensional analysis.