210 base 3 to 8

Answer 1

To convert the number 210 from base 3 to base 8, we can follow these steps:

1. Convert from base 3 to decimal (base 10): The digits in base 3 are multiplied by the powers of 3, from right to left.

   \[ 2 \times 3^2 + 1 \times 3^1 + 0 \times 3^0 \] \[ = 2 \times 9 + 1 \times 3 + 0 \times 1 \] \[ = 18 + 3 + 0 = 21 \]

2. Convert from decimal (base 10) to base 8: Now, we convert 21 from decimal (base 10) to base 8.

   Divide 21 by 8:

   • \(21 \div 8 = 2\) with a remainder of \(5\).

   So, we have:

   • The quotient is \(2\)
   • The remainder is \(5\)

   Now, we can represent \(21\) in base 8 as \(25_8\).

Thus, the base 3 number \(210_3\) is \(25_8\) in base 8.