The average human heart beats about 3.5×10^7times per year. The current population of Massachusetts is about 7×10^6people. 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, we can use the following formula:

\[ \text{Total heartbeats} = \text{Average heartbeats per person per year} \times \text{Population} \]

Given:

• Average heartbeats per person per year = \(3.5 \times 10^7\)
• Population of Massachusetts = \(7 \times 10^6\)

Now, we can calculate the total heartbeats:

\[ \text{Total heartbeats} = (3.5 \times 10^7) \times (7 \times 10^6) \]

Using the properties of exponents, we can multiply the coefficients and add the exponents:

\[ \text{Total heartbeats} = (3.5 \times 7) \times (10^7 \times 10^6) = 24.5 \times 10^{13} \]

Now, we need to convert \(24.5\) into scientific notation:

\[ 24.5 = 2.45 \times 10^1 \]

Thus, we adjust our expression:

\[ 24.5 \times 10^{13} = 2.45 \times 10^1 \times 10^{13} = 2.45 \times 10^{14} \]

Therefore, the total number of heartbeats in Massachusetts per year is:

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