To find the total number of heartbeats that occur in Massachusetts per year, we can multiply the average number of heartbeats per year by the population.
Given:
- Average heartbeats per person per year = \(3.5 \times 10^{67}\)
- Population of Massachusetts = \(7 \times 10^6\)
Now, we can set up the multiplication:
\[ \text{Total heartbeats} = \text{Average heartbeats per person} \times \text{Population} \]
\[ \text{Total heartbeats} = (3.5 \times 10^{67}) \times (7 \times 10^6) \]
We can multiply the coefficients (3.5 and 7) and then add the exponents of the powers of ten:
\[ = (3.5 \times 7) \times (10^{67} \times 10^6) \]
Calculating the coefficients:
\[ 3.5 \times 7 = 24.5 \]
Now, calculating the powers of ten:
\[ 10^{67} \times 10^6 = 10^{67 + 6} = 10^{73} \]
Now, we can combine these results:
\[ \text{Total heartbeats} = 24.5 \times 10^{73} \]
To express this in proper scientific notation, we adjust \(24.5\) to \(2.45\) by moving the decimal one place to the left, and increase the exponent by 1:
\[ = 2.45 \times 10^{74} \]
Thus, the total number of heartbeats that occur in Massachusetts per year is
\[ \boxed{2.45 \times 10^{74}} \]
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