The other day I had to calculate 1.26^3 and I was thinking about the quickest way to mentally do this.

I realized that the following method is rare and needs to be talked about. It is extremely fast.

Here is how I did this.

First step. Think of 126, divide by 4 and add this to 126:

126 = 120 + 6, so division by 4 is easy: 30 + 1.5 = 31.5

Add 31.5 to 126 and get 157.50.

Second step. Add 1% of 126 = 1.26.

157.50 + 1.26 = 158.76.

Except for the decimal point, this is 126 squared!

Now multiply 1.5876 by 1.26. Same routine:

Divide 158.76 by 4:

158 = 160 - 2, so division by 4 gives 40 - 0.5 = 39.50

Add this to 158.76 gives 198.26.

Quickest way is to first add 40 to 158.76 and then subtract 0 5.

Now divide 0.76 by 4.

76 = 80 - 4

(80 - 4)/4 = 20 - 1 = 19

So add 19 cents and get 198.45

Now add 1.5876 (1% of 158.76):

The complement of 198.45 is 1.55.

Add that first.

198.45 + 1.5876 =198.45 + 1.55 +0.0376 = 200.0376

So 1.26^3 = 2.000376.

The whole idea is that adding a quarter is the same as multiplying by 1.25.

Since we are multiplying by 1.26 instead of 1.25, we need to also add a percent.