Property 3
If a number in decimal counting system is to be written in another system, the number is divided to the base value of the desired system. This operation continues until the quotient is smaller than the divisor. In divisions with remainders, the last quotient and the remainders are written in reverse order. In divisions with remainders, the remainders are written in reverse order.
\(35=(x)_{4}\)
\(\Rightarrow35=(203)_{4}\)
1.
\(27=(x)_{2}\)
\(\Rightarrow x=?\)
2.
\(1515=(x)_{5}\)
\(\Rightarrow x=?\)
3.
\(24=(x)_{6}\)
\(\Rightarrow x=?\)
4.
\(306=(x)_{3}\)
\(\Rightarrow x=?\)
5.
\((54)_{6}=(x)_{5}\)
\(\Rightarrow x=?\)
6.
\((53)_{6}=(x)_{7}\)
\(\Rightarrow x=?\)
7.
\((36)_{7}=(3x)_{8}\)
\(\Rightarrow x=?\)
8.
\((321)_{4}=(x)_{5}\)
\(\Rightarrow x=?\)
9.
\((408)=(ababc)_{4}\)
\(\Rightarrow a\cdot b=?\)
10.
\((52)_{6}=(2xx)_{4}\)
\(\Rightarrow x=?\)
11.
\(2\cdot3^5+3^2+2=(x)_{3}\)
\(\Rightarrow x=?\)
12.
\(a>4\)
\(3a^4+2a^3+4a+2=(x)_{a}\)
\(\Rightarrow x=?\)
13.
\(3\cdot6^2+2\cdot6+3+\samefrac{1}{6}=(A)_{6}\)
\(\Rightarrow A=?\)