n2739178 wrote:

Hi all,

Does anyone know of a shortcut for squaring, or cubing, a decimal greater than 1 such as 1.04, rather than manually multiplying 1.04 * 1.04. This would be specifically handy for quick Compound Interest calculations.

I tried doing something like (1.04) squared = 104*104 then put the decimal point back in 4 places but I'm wondering if there is another, faster way to do this. I tried doing 1squared + .04squared as (1.04)squared which when distributed out is 1squared + .04squared but it returned the wrong result (i.e. 1 + 0.0016 = 1.0016) instead of 1.0816 which is the correct answer of 1.04squared.

There may be no quicker way than actually doing the math but if there is, would love to know it!

thanks

Ah! Finally! Something I'm actually good at!!! (pattern recognition) I have a psychological condition that lets me find patterns really quickly, but I have a hard time explaining them. Let me take a shot at this...

I'm doing this on the fly, so feel free to correct any wrong figures I come up with:

\(1.01 ^2 = 1 . (01*2) (01^2) = 1.0201\)

\(1.02^2 = 1 . (02*2) (02^2) = 1.0404\)

\(1.03^2 = 1 . (03*2) (03^2) = 1 . 06 09\)

\(1.04^2 = 1 . (04*2) (04^2) = 1 . 08 16\)

Things get a bit more interesting when you get into higher numbers...

If you get a three digit number as your square (like 10^2 = 100), then shift the ENTIRE number into the HUNDREDTHS place (2nd digit after decimal point). It's like you're shifting the entire three digit number ONE SPOT to the left, and adding any values that overlap.

\(1.10^2 = 1 . (10*2) (10^2) = 1 . 20 + 100\) (shift 100 one space left)\(= 1 . 2 (0+1) 00 = 1.2100\)

\(1.11^2 = 1 . (11*2) (11^2) = 1 . 22 + 121\) (shift 121 one space left)\(= 1 . 2 (2+1) 21 = 1.2321\)

\(1.12^2 = 1 . (12*2) (12^2) = 1 . 24 + 144\) (shift 144 one space left)\(= 1 . 2 (4+1) 44 = 1.2544\)

Does this make sense?