Final answer:
To convert 122 from base five to decimal, multiply each digit by five raised to the power of its position, starting from the right. The conversion follows as 2*(5^0) + 2*(5^1) + 1*(5^2), which adds up to 37 in decimal.
Step-by-step explanation:
The student has asked to express the number 122 in base five (122five) as a decimal number. To convert the number from base five to decimal, we multiply each digit of the base five number by five raised to the power of its position, starting from the right (which is position 0) and moving to the left.
Here's how we do it step by step:
- Take the rightmost digit (which is in the 'ones' place or 50), which is a 2. Multiply this by 50 (which is 1). That gives us 2 x 1 = 2.
- Move to the left to the next digit (which is in the 'fives' place or 51), which is also a 2. Multiply this by 51 (which is 5). That gives us 2 x 5 = 10.
- Finally, take the leftmost digit (which is in the 'twenty-fives' place or 52), which is a 1. Multiply this by 52 (which is 25). That gives us 1 x 25 = 25.
Add up the results of each step to get the total in decimal: 2 + 10 + 25 = 37.
Therefore, the number 122five expressed in the decimal system is 37.