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For example, I wanted to multiply 0.56 by 350 in my head(I was in bed and couldn't be bothered to find my calculator), so I made it into 56x3.5, then 28x7, then 7x4x7, then 49x4 to get the answer of 196.
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Interesting. Mentally, I break that problem down first into 350 * (0.5 + 0.06) = (350/2) + 350*6/100. The first half is easy, 175, and I can push that off to side mentally to work the next part. 350*6/100 is the same as 350/100*6, or 3.5*6. This is just 3*6 + 6/2, or 18+3=21. Add that to 175 and you get the answer, 196.
The best trick I pulled off was to take a physics test when the professor wanted all answers in final computed form (rounded to the nearest significant figure). Unfortunately, I had forgotten my scientific calculator that day. Fortunately, I remembered a method to compute the square root of any decimal number using an algorithm similar to long division (
not Newton's method, something else). Saved my ass.
There's nowhere I can't reach.