Question

Which will be the exponent of the common factor when finding the sum of (4.15 × 10⁻³) and (5.28 × 10⁶)?

a) (10⁻³)
b) (10⁶)
c) (10³)
d) (10⁹)

Answer 1

When finding the sum of (4.15 × 10^-3) and (5.28 × 10^6), the exponent of the common factor will be 10^6, option (b).

Step-by-step explanation:

The question you've asked is about determining the exponent of the common factor when adding the numbers (4.15 \u00d7 10^-3) and (5.28 \u00d7 10^6). When we add numbers in scientific notation, we need to have the same exponent for the powers of 10. As the two given numbers have different exponents (-3 and 6), we must adjust them to have the same exponent before we can add the decimal parts.

It is generally easier to adjust the number with the smaller exponent to match the one with the larger exponent. In this case, we would convert (4.15 \u00d7 10^-3) to have an exponent of 6, which would significantly change its decimal part (making it much smaller), so it wouldn't have a noticeable effect on the sum. Therefore, the exponent of the common factor after the sum will be 10^6, which is option (b).