sscritic wrote:To test your method, whatever it is, try it on $368,462 rather than $300,000.

I always try to transform the problem into an easier one, by some approximation, and then fix up

the approximation as many times as I need to get better estimates.

I worked this out on my own, but later found out it is called iterative refinement.

You migt find all this convoluted, but the idea is not to worry about slight inaccuracies, they

get corrected later, but to concentrtae on numbers you can keep in your head.

.07% of $368,462 in my head?

First estimate:

I recognize 368,462 as close to 1/3 of $1.1 Million

.07% of $1.1 million is .7% of $0.11M

or .7% of $110K =

7% of 11,000

= 7 times 110

=770.

Now I earlier tripled the original $368,462, so $770 is too high by a factor of 3,

dividing by 3 gives me $256.67.

This is the initial estimate. Which is often good enough to know I am in the ballpark.

Seond estimate (first refinement):

If I want to make this now more accuate, I recognize that my initial approximation

of 368,462 as 1/3 of $1.1M was low, since 366,667 is 1/3 of $1.1M, when rounded to the nearest dollar,

So my final answer was to low by a factor of (368,462-366,667)/366,667 which is about 1,800/360,000 or 1/200,

so I should adjust the 256.67 up by

1/2 of 2.5667 which is about

$1.28, so

256.67+1.28 is $257.95.

Thrid estimate (second refinemnet):

I could do this once again recognizing that the correction that I applied was slighly high, because 366,667 is not the same as

360,000. 6,667 out of 360,000 is 1111* 6 parts of 360,000 or 1111* 1 part in 60,000 = 1111/60,000 = 1.111 * 1/6th of 1/10 or 1 part in 60.

So my correction of 1.28 was high by a little over 2 cents.

So the third, more accurate estimate is

$257.95 - $.02 = $257.93

This is quite close to the actual $257.92

Is this the way you approach this problem , sscritic?