Question

A healthy human heart beats about 1,533,000 times in a year. A sparrow's heart beats about 241,776,000 times in a year.
About how many times faster does the sparrow's heart beat compared to the human heart?
Estimate using a single digit times a power of 10.
2×1082×106=1×102
or about 100 times faster
2×1092×106=1×103
or about 1,000 times faster
2×1082×105=1×103
or about 1,000 times faster
2×1092×105=1×104
or about 10,000 times faster

Answer 1

To compare the heartbeats of a sparrow to that of a human, we start with the numbers given:

- Human heart beats in a year: \(1,533,000\)
- Sparrow heart beats in a year: \(241,776,000\)

Next, we calculate how many times faster the sparrow's heart beats compared to the human heart. We do this by dividing the number of beats of the sparrow's heart by the number of beats of the human heart:

\[
\text{Ratio} = \frac{241,776,000}{1,533,000}
\]

Now let's simplify that division.

First, we can rewrite both numbers in scientific notation:

- \(1,533,000 \approx 1.533 \times 10^6\)
- \(241,776,000 \approx 2.41776 \times 10^8\)

Now perform the division:

\[
\text{Ratio} \approx \frac{2.41776 \times 10^8}{1.533 \times 10^6}
\]

This simplifies to:

\[
\text{Ratio} \approx \frac{2.41776}{1.533} \times \frac{10^8}{10^6} = \frac{2.41776}{1.533} \times 10^{8-6} = \frac{2.41776}{1.533} \times 10^2
\]

Calculating \(\frac{2.41776}{1.533}\):

\[
\frac{2.41776}{1.533} \approx 1.577
\]

Thus:

\[
\text{Ratio} \approx (1.577) \times 10^2 \approx 1.58 \times 10^2
\]

So this indicates that the sparrow's heart beats approximately:

\[
158 \text{ times faster than the human heart.}
\]

Since we are looking to estimate using a single digit times a power of 10, we can round \(1.58\) to approximately \(2 \times 10^2\).

Finally, in order to answer your question:

- Therefore, the sparrow's heart beats about \(100\) times faster than the human heart.

So, the correct estimation is:

**2×10² (about 100 times faster)**.