To determine the next whole number after 3355 in the base-six system, we need to consider the digits and their values in base six.
In the base-six system, the digits range from 0 to 5. After 5, the next digit is 10, representing six in decimal. Each place value in the base-six system follows the pattern: 1s, 6s, 36s, 216s, and so on.
Let's break down the number 3355 in the base-six system:
3 * 6^3 + 3 * 6^2 + 5 * 6^1 + 5 * 6^0 = 3 * 216 + 3 * 36 + 5 * 6 + 5 * 1 = 648 + 108 + 30 + 5 = 791
So, in the base-six system, the number 3355 is equal to 791 in decimal.
To find the next whole number after 3355 in the base-six system, we need to increment the least significant digit (the rightmost digit). Since the rightmost digit is 5, the next whole number in base six will be obtained by incrementing this digit by 1.
Adding 1 to the rightmost digit (5) in base six results in 10, which is equivalent to 6 in decimal. Thus, the next whole number after 3355 in the base-six system is 3360.