Question

Suppose that a certain fortunate person has a net worth of $76.0 billion ($7.60×10107.60×1010). If his stock has a good year and gains $3.20 billion (3.20×1093.20×109) in value, what is his new net worth?

Answer 1

If someone's net worth is $76.0 billion and their stock gains $3.2 billion, their new net worth will be $79.2 billion. Expressed in scientific notation, the new net worth is $7.92 × 10^{10}. This demonstrates how scientific notation can be used in practical applications involving large numbers.

Step-by-step explanation:

The student's question pertains to calculating the new net worth of a person after their stock has increased in value. First, the student has noted the current net worth as $76.0 billion, which expressed in scientific notation is $7.60 × 10^{10}. After gaining $3.20 billion in value, which is $3.20 × 10^{9} in scientific notation, we need to add this to the original net worth. The new net worth, therefore, becomes:

$76.0 billion + $3.2 billion = $79.2 billion

Expressed in scientific notation, the new net worth is:

$7.60 × 10^{10} + $3.20 × 10^{9} = $7.92 × 10^{10}

This calculation shows that a gain in stock value, even when it's in the billions, can have a significant impact on someone's net worth. It is also a practical application of scientific notation in understanding large numbers.