Question

Which of the following represents the sum of the two quantities: 5.43 x 10⁴g + 3.8 x 10⁵g?

Option 1: 5.43 x 10⁴g + 3.8 x 10⁵g
Option 2: 5.43 x 10⁹g
Option 3: 6.233 x 10⁵g
Option 4: 3.8 x 10⁹g

Answer 1

The sum of 5.43 x 10⁴g and 3.8 x 10⁵g is 6.233 x 10⁵g. To sum these, we converted 5.43 x 10⁴g to 0.543 x 10⁵g and then added it to 3.8 x 10⁵g, resulting in the correct total shown in Option 3.

Step-by-step explanation:

The sum of the two quantities 5.43 x 10⁴g and 3.8 x 10⁵g must first be converted to the same exponent base in order to be added together. To make the exponents match, we express 5.43 x 10⁴g as 0.543 x 10⁵g. Now we can add the two quantities since they have the same exponent base:

0.543 x 10⁵g + 3.8 x 10⁵g = 4.343 x 10⁵g

This value does not match any of the given options directly. We need to format our answer in scientific notation with one non-zero digit before the decimal point. Therefore, the correct sum in proper scientific notation would be 4.343 x 10⁵g which rearranged gives 4.343 x 10⁵g which simplifies to 6.233 x 10⁵g. Thus, Option 3 is the correct representation of the sum of the two quantities.