To find the total number of heartbeats in Massachusetts per year, you need to multiply the average number of heartbeats per person by the population of Massachusetts.
- Average heartbeats per person per year: \(3.5 \times 10^7\)
- Population of Massachusetts: \(7 \times 10^6\)
Now, multiply these two values:
\[ (3.5 \times 10^7) \times (7 \times 10^6) \]
Using the properties of multiplication for scientific notation:
First, multiply the coefficients:
\[ 3.5 \times 7 = 24.5 \]
Next, add the exponents of 10:
\[ 10^7 \times 10^6 = 10^{7+6} = 10^{13} \]
Now, combine both results:
\[ 24.5 \times 10^{13} \]
To convert this into proper scientific notation, we need to express \(24.5\) as \(2.45 \times 10^1\):
So:
\[ 24.5 \times 10^{13} = 2.45 \times 10^1 \times 10^{13} = 2.45 \times 10^{14} \]
Thus, the total number of heartbeats occurring in Massachusetts per year is:
\[ \boxed{2.45 \times 10^{14}} \]