Determine the digit immediately to the left of the decimal point in the base ten representation of (3+√7)²⁰⁰⁴

**** For an extra challenge, solve this puzzle using only pen and paper.

The problem exceeds the precision needed in UBASIC. Miracle Calc gives an answer that doesn't live up to its promised precision.

Wolfram Alpha, if prodded to give more and more digits, eventually gets to digits beyond the power of 10 of its scientific notation, but as soon as you get that far into the number the varied digits stop varying and all the remaining digits are 9's. In carefully counting off positions to the right of the decimal in the amount of the power of ten, it does place the decimal between the last non-9 digit and the first 9 of the all-9's, so it gives the semblance of what would be ...7.999999.... It would seem that Wolfram Alpha is rounding the result tot he nearest integer--a rather strange thing to do.  But in any instance that leaves us in a quandary as to whether the digit immediately to the left of the decimal point is a 7 or an 8, as the number apparently rounds to one ending in 8.

 

Posted by Charlie on 2013-08-24 16:38:26