Final answer:
To write 343 as a base five numeral, divide it by the largest powers of 5, working downwards, and use the remainders to determine the digits. The base five numeral for 343 is 2333.
Step-by-step explanation:
To write 343 as a base five numeral, we need to convert the number from base ten (our standard numbering system) to base five. In base five, each digit represents a power of 5, starting with 50 on the right and increasing to the left.
First, find the largest power of 5 that is less than or equal to 343. This is 53, which equals 125. Determine how many times 125 fits into 343, which is 2 times (250), leaving a remainder of 93.
Next, find the largest power of 5 that is less than or equal to 93, which is 52 or 25. It fits into 93 three times (75), leaving a remainder of 18.
Now, look for the largest power of 5 less than 18, which is 51 or 5. It fits three times with a remainder of 3.
Finally, with our remainder of 3, we note that it is already less than 5 and is thus the last digit in our base five numeral.
Putting it all together, the base five representation of 343 is 2333. So, to write 343 as a base five numeral, you would write it as 23335.