The average human heart beats about 3.5×10^7 times per year. The current population of Massachusetts is about 7×10^6 people. About how many heartbeats occur in Massachusetts per year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1

Answer 1

To find the total number of heartbeats occurring in Massachusetts per year, you multiply the average number of heartbeats per person by the population of Massachusetts.

Given:

• Average heartbeats per year per person = \(3.5 \times 10^7\)
• Population of Massachusetts = \(7 \times 10^6\)

Now, perform the multiplication:

\[ \text{Total heartbeats} = (3.5 \times 10^7) \times (7 \times 10^6) \]

When multiplying in scientific notation, you multiply the coefficients and add the exponents:

\[ = (3.5 \times 7) \times (10^7 \times 10^6) = 24.5 \times 10^{13} \]

Now, we want to express \(24.5\) in proper scientific notation:

\[ 24.5 = 2.45 \times 10^1 \]

Now substitute this back into the expression:

\[ 24.5 \times 10^{13} = 2.45 \times 10^1 \times 10^{13} = 2.45 \times 10^{14} \]

Thus, the total number of heartbeats occurring in Massachusetts per year is:

\[ \boxed{2.45 \times 10^{14}} \]