The most memorable math class I ever had in school saw a surprise test. It was simple math, but big, awkward numbers, and lots of them. The teacher told us that we would not have time to calculate them all (and calculators - to be honest, had not been invented yet). He told us that nearly all the math we would ever do in life would be used to make a decision. The result would direct us to a "yes" or a "no". So, if we were pressed for time, a close guess would probably result in the correct decision. The purpose of the test was for us to guess at the answer. If our guess was within 10% of the correct answer, we would get the mark
Many moons ago (before computer accounting software was available to small companies) I hired a lady who's primary job was to gather all the sales tax information for the different jobs and equipment sales we had done that month and compute the sales tax (VAT in UK) we had to remit to the government. At that time the company turnover was usually about $100,000 per month,the sales tax rate was 8.25% and almost all our sales were sales tax eligible. After her first month she walked in and presented me with a check for approximtley $84,000 to sign for mailing to the tax office. I asked her if we had had an unusally large sale that month (knowing we hadn't) to which she said no, revenue was just over $100,000. I suggested she check her math and she threw a wobbler about me questioning her professionalism and how rude it was of me to doubt her numbers based on her many years of being a accounting dept sales tax expert.
Bottom line, I thought to myself, is she cant start out with a ballpark number in her head and then work the actual figures that will verify her "guesstimate" then she is going to bankrupt me sooner or later and out the door she went.
Always start out with a rough mental calculation before working out the exact number.