Tricks For Quick Check Calculations
Rather than accept numbers given to me, I generally like to make sure that
they are at least reasonable. Some of my less mathematical friends agree
that this is a good idea, but complain that it's hard to do all those
calculations.
Fortunately, those calculations don't have to be hard. All you have to do is
get used to doing approximate (I call them 'quick check') calculations.
Remember, all you care about is whether the numbers are reasonable, not
whether they are exactly right. That means that your check does not need to
be very accurate, only close enough for you to know whether to be worried.
Below are several of the rules I've come across in my years of checking
other people's numbers. If you have any more, send them to
the Mathemagician to let me know.
Rules for quick check calculations:
 Forget the extra digits, round off to easy numbers
 Doubling 4 times adds 1 extra digit
 Doubling 10 times adds 3 extra digits
 Divide 72 by the interest rate to get the years for money to double
 Add the digits for divisibility by 9 (or 3)
 35% of the population have any uncommon (not unheardof) condition
Write to the Mathemagician if you have other
tricks for fast calculations.
Add the digits for divisibility by 9 (or 3)
If you want to find out if a number is divisible by 9, just add the digits.
If the result is more than one digit, then add the digits on that number.
Keep doing this until you have a single digit number.
If the single digit number is 9, then the original number was divisible by
9. If the single digit is 3 or 6, then the original number was not divisible
by 9, but was divisible by 3.
You can do a similar check for divisibility by eleven. Starting at the last
digit, subtract the second digit, then add the third digit, and so on,
alternating between adding and subtracting. If the result is zero, or a
multiple of eleven, then the original number was a multiple of eleven.
I have often admired the mystical way of Pythagoras, and the secret magic of
numbers.
 Sir Thomas Browne, 1643

Some useful number facts for quick checks.

Numbers in the real world.

Grannus' circle.

The front gate of Esmerel.
Page maintained by the Mathemagician.