Final answer:
5 x 10⁻⁷ is larger than 4.1 x 10⁻⁷ because the coefficient 5 is greater than 4.1, even though both numbers are multiplied by the same power of 10.
Step-by-step explanation:
To determine which number is bigger, 5 x 10⁻⁷ or 4.1 x 10⁻⁷, we can compare the coefficients since the powers of 10 are the same for both numbers. The coefficient 5 in 5 x 10⁻⁷ is larger than the coefficient 4.1 in 4.1 x 10⁻⁷. Therefore, 5 x 10⁻⁷ is the larger number.
Another way to determine the power of 10 in scientific notation is to count the number of places you need to move the decimal point to get a numerical value between 1 and 10. The number of places equals the power of 10. This number is positive if you move the decimal point to the right and negative if you move the decimal point to the left, but since both numbers have the same power of 10 in this question, only the coefficients need to be compared.