Final answer:
The numeral 3 in base-ten is equivalent to numeral 10 in base 3 because 3 can be expressed as 1 group of 31 and 0 groups of 30.
Step-by-step explanation:
To convert the base-ten numeral 3 to base 3, we use the concept of representing numbers with exponents and powers of the base. In base 3, each digit position represents a power of 3. Starting with the highest power of 3 that fits into the number without exceeding it, we find that the highest power of 3 that fits into 3 is 31 (which equals 3).
Since 3 can be represented as 1 group of 31, we write a 1 in the 31 position (which corresponds to the 'tens' position in base ten). We do not need any groups of the next lower power, which is 30 (which equals 1), so we write a 0 in the 30 (or 'ones') position. Thus, the base-ten numeral 3 is represented as the numeral 10 in base 3.
The correct answer to the question is a. 10.