Convert 202 base 3 to 8

Answer 1

To convert the number \(202\) in base \(3\) to base \(8\), we can follow these steps:

1. Convert from base \(3\) to base \(10\): The number \(202\) in base \(3\) can be converted to decimal (base \(10\)) using the positional value system: \[ 202_3 = 2 \cdot 3^2 + 0 \cdot 3^1 + 2 \cdot 3^0 \]

   • \(2 \cdot 3^2 = 2 \cdot 9 = 18\)
   • \(0 \cdot 3^1 = 0 \cdot 3 = 0\)
   • \(2 \cdot 3^0 = 2 \cdot 1 = 2\)

   Adding these values together: \[ 18 + 0 + 2 = 20 \] So, \(202_3 = 20_{10}\).

2. Convert from base \(10\) to base \(8\): Now we will convert \(20_{10}\) to base \(8\). We do this by dividing by \(8\) and keeping track of the remainders:

   • \(20 \div 8 = 2\) remainder \(4\)
   • \(2 \div 8 = 0\) remainder \(2\)

   Now we read the remainders from bottom to top to get the base \(8\) representation. Thus, \(20_{10} = 24_{8}\).

In summary, the base \(3\) number \(202\) converts to \(24\) in base \(8\).

So, the final answer is: \[ 202_3 = 24_8 \]