⟩ 194 base 10= ___ base 5The base 5 representation of the decimal number 2048 is______?
2048 to base 10:-
2 ["add" the next (first) digit]
2 * 10 = 20 [multiply by the base]
20 + 0 = 20 [add the next digit]
20 * 10 = 200 [multiply by the base]
200 + 4 = 204 [add the next digit]
204 * 10 = 2040 [multiply by the base]
2040+ 8 = 2048 [add the next digit]
??? to base 5:-
3
3* 5 = 15 [multiply by the base]
15+1 = 16 [add the next digit]
16* 5 = 80 [multiply by the base]
80+ 1 = 81 [add the next digit]
81* 5 = 405 [multiply by the base]
405+ 4 = 409 [add the next digit]
409*5 = 2045
2045+3 = 2048
since both the answers tally i.e., 2048==2048
hence the no. 31143 is the ans..
