# Fast arithmetic, without a calculator?

This has been on my mind for quite a while now... Is it really crucial to be able to crunch numbers on the fly?

I have considerate difficulty making out the quotient of $1 / 0.732$ for example. I can approximate it well, but still (~1.3...). When I go for precision, I am too slow.

Are there techniques to accelerate arithmetic operations?

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 Related... – J. M. Sep 8 '11 at 19:18 "Is it really crucial to be able to crunch numbers on the fly?" - well it's sorta kinda embarrassing for me to take long in figuring out how much change I ought to be getting, or reckoning how much to tip the waitress. Otherwise... – J. M. Sep 8 '11 at 19:21 Well, that's not really a problem... But more intensive operations, indeed, drag me down. – Curiosity Sep 8 '11 at 19:24 Crucial for what? It can be useful in some circumstances, but it really depends on your career goals. A mathematician doesn't really need it, although occasionally mental arithmetic can come in handy in a calculus lecture. – Robert Israel Sep 8 '11 at 23:53

Doerfler's book Dead Reckoning: Calculating Without Instruments contains algorithms specifically designed for computing nontrivial things mentally. But it's still not easy and requires quite a lot of practice, I guess. To begin with, one must be really good at multiplying two-digit numbers (so I'm lost there already...).

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