Final answer:
To add the base 5 numerals 23203₅ and 31420₅, each column is added together and carries are applied wherever the sum is 5 or more. The final sum of these two numbers in base five is 203023₅.
Step-by-step explanation:
The question requires us to add two base 5 numerals: 23203₅ and 31420₅. Similar to addition in base ten, we add the digits column by column, starting from the rightmost column and moving to the left. We also need to carry over if the sum of a column is 5 or greater, since 5 is the base in this system and such a sum would be represented with a carry to the next left column. Let's perform the addition:
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- 3 (from the first number) + 0 (from the second number) = 3 (write 3 under the units column).
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- 0 + 2 = 2 (write 2 under the next column).
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- 3 + 4 = 12 in base ten, but in base five, this is written as 22₅, so we write 2 and carry over 2.
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- 2 (carried over) + 2 + 1 = 10 in base ten, which is 20₅ in base five, so we write 0 and carry over 2 again.
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- 2 (carried over) + 3 + 3 = 13 in base ten, which is written as 23₅ in base five, so the final result is 3 and carry over 2 again.
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- Finally, we add the carried over 2 to the leftmost column: 2 + 0 = 2.
Piecing it all together, the sum of 23203₅ and 31420₅ in base five is
203023₅
.