To find the total number of heartbeats that occur in Massachusetts per year, we can multiply the average number of heartbeats per person per year by the population of Massachusetts.
- The average number of heartbeats per person per year is \(3.5 \times 10^7\).
- The population of Massachusetts is \(7 \times 10^6\).
Now, we can calculate the total heartbeats:
\[ \text{Total heartbeats} = (3.5 \times 10^7) \times (7 \times 10^6) \]
Now, we can multiply the coefficients (the numbers in front) and then add the exponents (the powers of 10):
\[ 3.5 \times 7 = 24.5 \]
For the powers of 10:
\[ 10^7 \times 10^6 = 10^{(7+6)} = 10^{13} \]
Combining both parts:
\[ \text{Total heartbeats} = 24.5 \times 10^{13} \]
Now, to express \(24.5\) in proper scientific notation, we convert it to \(2.45\) and adjust the exponent:
\[ 24.5 = 2.45 \times 10^1 \]
So,
\[ 24.5 \times 10^{13} = 2.45 \times 10^1 \times 10^{13} = 2.45 \times 10^{14} \]
Therefore, the total number of heartbeats that occur in Massachusetts per year is:
\[ \boxed{2.45 \times 10^{14}} \]