Editing Sanity check (section)

===Mathematical===
A sanity test can refer to various [[order of magnitude|orders of magnitude]] and other simple [[rule of thumb|rule-of-thumb]] devices applied to cross-check [[mathematics|mathematical]] [[calculations]]. For example:
*If one were to attempt to [[square (algebra)|square]] 738 and calculated 54,464, a quick sanity check could show that this result cannot be true. Consider that {{awrap|1=700 < 738,}} yet {{awrap|1=700{{sup|2}} = 7{{sup|2}} × 100{{sup|2}} =}} {{awrap|1=490,000 > 54,464.}} Since squaring positive integers preserves their [[Inequality (mathematics)#Applying a function to both sides|inequality]], the result cannot be true, and so the calculated result is incorrect. The correct answer, {{awrap|1=738{{sup|2}} = 544,644,}} is more than 10 times higher than 54,464.
*In multiplication, {{awrap|1=918 × 155}} is not 142,135 since 918 is divisible by three but 142,135 is not (digits add up to 16, not a [[3#Mathematics|multiple of three]]). Also, the product must end in the same digit as the product of end-digits: {{awrap|1=8 × 5 = 40,}} but 142,135 does not end in "0" like "40", while the correct answer does: {{awrap|1=918 × 155 = 142,290.}} An even quicker check is that the product of even and odd numbers is even, whereas 142,135 is odd.