To determine the total number of heartbeats in Massachusetts per year, we can multiply the average number of heartbeats per person per year by the population.
Given:
- Average heartbeats per year per person = \(3.5 \times 10^7\)
- Population of Massachusetts = \(7 \times 10^6\)
Total heartbeats in Massachusetts per year:
\[ \text{Total heartbeats} = \text{heartbeats per person} \times \text{population} \]
\[ \text{Total heartbeats} = (3.5 \times 10^7) \times (7 \times 10^6) \]
Now, we can multiply the coefficients (3.5 and 7) and add the exponents of the powers of 10:
\[ \text{Total heartbeats} = 3.5 \times 7 \times 10^{7 + 6} \] \[ = 24.5 \times 10^{13} \]
To express \(24.5\) in scientific notation, we convert it to \(2.45\) by shifting the decimal point one place to the left. This increases the exponent of \(10\) by 1:
\[ = 2.45 \times 10^{14} \]
Therefore, the total number of heartbeats that occur in Massachusetts per year is:
\[ \boxed{2.45 \times 10^{14}} \]