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.Often, however,all you ll want is a ballpark estimate.Say you re getting quotesfrom different lenders on refinancing your home.All you reallyneed at this information-gathering stage is a ballpark estimateof what your monthly payments will be.Or say you re settling arestaurant bill with a group of friends and you don t want to fig-ure each person s bill to the penny.The guesstimation methodsdescribed in this chapter will make both these tasks and manymore just like them much easier.Addition, subtraction, divi-sion, and multiplication all lend themselves to guesstimation.Asusual, you ll do your computations from left to right.ADDITION GUESSTIMATIONGuesstimation is a good way to make your life easier when thenumbers of a problem are too long to remember.The trick is toround the original numbers up or down: Benj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 109Good Enough: The Art of Guesstimation 1098,367 8,0005,819 ª 6,00014,186 14,000(ª means approximately)George Parker Bidder: The Calculating Engineerhe British have had their share of lightning calculators, and theTmental performances of George Parker Bidder (1806 1878), bornin Devonshire, were as impressive as any.Like most lightning calcula-tors, Bidder began to try his hand (and mind) at mental arithmetic asa young lad.Learning to count, add, subtract, multiply, and divide byplaying with marbles, Bidder went on tour with his father at age nine.Almost no question was too difficult for him to handle. If themoon is 123,256 miles from the earth and sound travels four miles aminute, how long would it take for sound to travel from the earth tothe moon? The young Bidder, his face wrinkled in thought for nearlya minute, replied, Twenty-one days, nine hours, thirty-four minutes. (We know now that the distance is closer to 240,000 miles andsound cannot travel through the vacuum of space.) At age ten, Biddermentally computed the square root of 119,550,669,121 as 345,761 ina mere thirty seconds.In 1818, Bidder and the American lightning cal-culator Zerah Colburn were paired in a mental calculating duel inwhich Bidder, apparently, outnumbered Colburn.Riding on his fame, George Bidder entered the University of Edin-burgh and went on to become one of the more respected engineersin England.In parliamentary debates over railroad conflicts, Bidderwas frequently called as a witness, which made the opposition shud-der; as one said, Nature had endowed him with particular qualitiesthat did not place his opponents on a fair footing. Unlike Colburn,who retired as a lightning calculator at age twenty, Bidder kept it upfor his entire life.As late as 1878, in fact, just before his death, Biddercalculated the number of vibrations of light striking the eye in onesecond, based on the fact that there are 36,918 waves of red light perinch, and light travels at approximately 190,000 miles per second. Benj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 110110 Secrets of Mental MathNotice that we rounded the first number down to the nearestthousand and the second number up.Since the exact answer is14,186, our relative error is small.If you want to be more exact, instead of rounding off to thenearest thousand, round off to the nearest hundred:8,367 8,4005,819 ª 5,80014,186 14,200The answer is only 14 off from the exact answer, an error ofless than.1%.This is what I call a good guesstimation!Try a five-digit addition problem, rounding to the nearesthundred:46,187 46,20019,378 ª 19,40065,565 65,600By rounding to the nearest hundred, our answer will alwaysbe off by less than 100.If the answer is larger than 10,000, yourguesstimate will be within 1% of the exact answer.Now let s try something wild:23,859,379 24,000,000 23.9 million7,426,087 ª 7,000,000 or 7.4 million31,285,466 31,000,000 31.3 millionIf you round to the nearest million, you get an answer of 31million, off by roughly 285,000.Not bad, but you can do betterby rounding to the nearest hundred thousand, as we ve shownin the right-hand column.Again your guesstimate will be within Benj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 111Good Enough: The Art of Guesstimation 1111% of the precise answer.If you can compute these smallerproblems exactly, you can guesstimate the answer to any addi-tion problem.Guesstimating at the SupermarketLet s try a real-world example.Have you ever gone to the storeand wondered what the total is going to be before the cashierrings it up? For estimating the total, my technique is to roundthe prices to the nearest 50¢
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