Decimal digits vs integer digits

[Dieter]

(02-21-2018 11:22 AM)pier4r Wrote:  For the little that I know, while we may extract hundreds/thousands of decimal digits for a square root with our calculators, getting the same for an integer number is not always that easy.

I don't know why you distinguish between the digits left and right of the decimal point. Let's say you want to calculate

11^32 = 2111377674535255285545615254209921

This is an integer. But is this really more complicated than

1,1^32 = 21,11377674535255285545615254209921

If it is, simply calculate the latter and shift the decimal point. ;-)

(02-21-2018 11:22 AM)pier4r Wrote:  Dunno compute 345^678 , this may be a number that would require quite a lot of work for a lot of calculators (maybe not the prime/50g).

345^678 = 10^(678 * lg 345). The term in brackets is 678*2,5378... = 1720,6413..., so if calculating with many decimal digits is easy, this is easy as well. Take the fractional part of the result, i.e. 0,6413... (look, only decimal digits, that must be easy ;-)) and determine the antilog 4,3787... – and you already got the result 4,3787...E+1720. You just need the mantissa (4,3787...) with 1720 decimal digits. Which, you say, is not too difficult.

OK, OK – I think you got the idea. ;-)
No, I do not think that integers are easier or harder than decimals.

Dieter