To find the total number of heartbeats that occur in Massachusetts per year, we'll multiply the average number of heartbeats per heart per year by the population of Massachusetts.
Given:
- Average heartbeats per year = \( 3.5 \times 10^7 \)
- Population of Massachusetts = \( 7 \times 10^6 \)
Now we multiply these two quantities:
\[ \text{Total heartbeats} = (3.5 \times 10^7) \times (7 \times 10^6) \]
Using the properties of multiplication (specifically \(a \times b = (a \times c) \times (b \times d)\)), we can rearrange it:
- Multiply the coefficients: \(3.5 \times 7 = 24.5\)
- Add the exponents of 10 in the scientific notation: \(10^7 \times 10^6 = 10^{7+6} = 10^{13}\)
Now we combine these results:
\[ \text{Total heartbeats} = 24.5 \times 10^{13} \]
To express this in proper scientific notation, we can move the decimal point in 24.5 one place to the left:
\[ 24.5 = 2.45 \times 10^1 \]
Now, we substitute this back into our multiplication:
\[ 24.5 \times 10^{13} = (2.45 \times 10^1) \times 10^{13} = 2.45 \times 10^{1 + 13} = 2.45 \times 10^{14} \]
Thus, the total number of heartbeats that occur in Massachusetts per year is:
\[ \boxed{2.45 \times 10^{14}} \]