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