Final answer:
Calculate 5.3 x 10⁹ + 14.5 x 10⁵, convert 14.5 x 10⁵ to match the exponent of 10⁹, becoming 0.00145 x 10⁹. Add the mantissas to get 5.30145, and the final answer in scientific notation is 5.30145 x 10⁹.
Step-by-step explanation:
To calculate the expression 5.3 x 10⁹ + 14.5 x 10⁵, we must keep in mind that when adding numbers in scientific notation, we first need to have the same exponent for both terms. Since the exponents are different, we cannot directly add the numbers. We can, however, convert one of the terms to match the exponent of the other, and then add the mantissas (numbers in front of the 10).
Step 1: Convert 14.5 x 10⁵ to the power of 10⁹. To do this, we move the decimal point four places to the left (since we're increasing the exponent from 10⁵ to 10⁹) and get 0.00145 x 10⁹.
Step 2: Now that both terms are in the form of x times 10⁹, we can add the mantissas: 5.3 + 0.00145 = 5.30145
Step 3: The final step is to write the sum in scientific notation: 5.30145 x 10⁹
Therefore, the original expression 5.3 x 10⁹ + 14.5 x 10⁵ equals 5.30145 x 10⁹ when expressed in proper scientific notation.