Final answer:
When multiplying two numbers in scientific notation, multiply the coefficients and add the exponents of 10. So, the correct answer is option b.
Step-by-step explanation:
When multiplying two numbers written in scientific notation, you multiply the coefficients (the numbers out front) and add the exponents of 10 together. For example, if you were to multiply (3 × 105) by (2 × 100), you would first multiply the coefficients, which are 3 and 2, to get 6. Then, you would add the exponents, which are 5 and 0, resulting in 5. So, the answer would be 6 × 105.
To illustrate further, if we use different exponents, for instance, (4 × 102) × (5 × 103), we would multiply 4 and 5 to get 20, and then add the exponents 2 and 3 to get 5, resulting in an answer of 20 × 105. However, this is not proper scientific notation because the coefficient (20) is not between 1 and 10. We would need to adjust it to 2.0 and increment the exponent by 1 to get 2.0 × 106, which now is in proper scientific notation.
So, the correct method of handling exponents when multiplying in scientific notation is to add the exponents.