Question

okay so convert the following numbers in base 10 to numbers in other bases as indicated:
convert 345 in base 10 to an equivalent number in base 4!

Answer 1

so i divided 345 by 4 and got 86.25 but how do you get the remainder

Answer 2

\[345_{10}=3\times10^2+4\times10^1+5\times10^0\]

Answer 3

\[345_{4}=a\times4^4+ b\times4^3+c\times4^2+d\times4^1+e\times4^0\]

Answer 4

\[345/4^4=345/256=1+89/256\]
so \(a=1\)

\[89/4^3=89/64=1+25/64\]
so \(b=1\)

\[25/4^2=25/16=1+9/64\]
so \(c=1\)

\[9/4^1=9/4=2+1/4\]
so \(d=2\)

\[1/4^0=1/1=1\]
so \(d=1\)