Convert 43.212₅ to base ten.

Explanation

For the whole number part 43 in base 5: the 4 is in the fives place and 3 is in the ones place. Calculate: 4 times 5¹ plus 3 times 5⁰ equals 20 plus 3 equals 23 in base 10.

For the decimal part .212 in base 5: multiply each digit by the appropriate negative power of 5. First digit: 2 times 5 to the negative 1 equals 2 over 5 equals 0.4. Second digit: 1 times 5 to the negative 2 equals 1 over 25 equals 0.04. Third digit: 2 times 5 to the negative 3 equals 2 over 125 equals 0.016.

Add the decimal parts: 0.4 plus 0.04 plus 0.016 equals 0.456. Combine with whole number: 23 plus 0.456 equals 23.456 in base 10.