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.
Given:
- Average heartbeats per year per person = \( 3.5 \times 10^7 \)
- Population of Massachusetts = \( 7 \times 10^6 \)
The total heartbeats in Massachusetts per year is calculated as follows:
\[ \text{Total heartbeats} = \text{Heartbeats per person} \times \text{Population} \]
\[ = (3.5 \times 10^7) \times (7 \times 10^6) \]
Using the properties of multiplication with scientific notation, we can multiply the coefficients and add the exponents:
\[ = 3.5 \times 7 \times 10^{7+6} \]
Calculating \( 3.5 \times 7 \):
\[ 3.5 \times 7 = 24.5 \]
Now adding the exponents:
\[ = 24.5 \times 10^{13} \]
Since we need to express this in standard scientific notation, we can express \( 24.5 \) as \( 2.45 \times 10^1 \). Therefore:
\[ = 2.45 \times 10^1 \times 10^{13} \]
Combining the powers of ten:
\[ = 2.45 \times 10^{14} \]
Thus, the total number of heartbeats that occur in Massachusetts per year is
\[ \boxed{2.45 \times 10^{14}} \]