how would you convert 32.42 base 5 to base 10? i can figure it out with just the decimal part but i dont know what to do know that there's a whole number. do i do it seperately or together? also another one similar is 11 1/2 to base 4.
separate whole and decimal, convert to base 10, add back together
32.42 base 5 32 ---> 17 .42 ---> 22/25 --> .88
17.88
11.2 base 4 (.2 not .5 i think) 11 ---> 5 .2 ---> 1/2 5 1/2 fraction stays the same when going to bigger bases, but it might change when going to smaller bases - not sure about that though
Another interesting thing which might be easily brought out concerning bases and fraction are repeated fractions in a different base. For example, change .33333... in base 5 to base 10. The shortcut lies in converting the repeated fraction into the sum of an infinite converging geometric series. Videlicet, .3333.... in base 5 is 3/5+3/25+3/125+3/625+..., then just use the formula for the infinited series. Ergo .33.. base 5 = 3/5 / 4/5 = 3/4. Best Wishes
