Final answer:
The correct numerals for the words given are 12,241 and 2,500, option a. Scientific notation involves writing a number between 1 and 10 multiplied by a power of 10. This allows us to express very large or small numbers in a simplified format.
Step-by-step explanation:
To answer the student's question, the numerals for 'Twelve thousand two hundred forty-one' and 'two thousand five hundred' are written respectively as 12,241 and 2,500. Hence, the correct option is a. Twelve thousand two hundred forty-one; two thousand five hundred.
Moving on to the concept of scientific notation, which is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, we need to follow specific rules. This requires the number to be written as a product of a number between 1 and 10 and a power of 10.
8,099 x 107 would be correctly written as 8.099 x 1010 in scientific notation because the decimal point has been moved three places to the left to place the first non-zero digit at the beginning.
34.5 x 100 is already in scientific notation as the number is between 1 and 10 and followed by a power of 10.
0.000332 × 104 should be written as 3.32 x 100 as the decimal is moved five places to the right.
In summary, when writing numbers in scientific notation, move the decimal point to the right or left to get a number between 1 and 10 and adjust the exponent on the 10 accordingly. The exponent increases when the decimal moves to the left and decreases when the decimal moves to the right.