Question

Multiply in Scientific Notation Practice
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Question
The average human heart beats about 3.5×107
times per year. The current population of Massachusetts is about 7×106
people. About how many heartbeats occur in Massachusetts per year? Write the answer in scientific notation. Express the answer to the exact decimal place.

Answer 1

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:

\[
\boxed{2.45 \times 10^{14}}
\]