Question

The distance a tortoise moves in one minute was measured in miles. The tortoise traveled 2.37×10−9 miles. Use scientific notation to convert the distance to inches. Write your answer using scientific notation. Round the decimal portion of your answer to the nearest hundredth.

Note: 1 mile is equal to 63,360 inches.

Answer 1

condense it please

Answer 2

To convert the distance a tortoise traveled from miles to inches, we start with the distance it traveled in miles, which is \( 2.37 \times 10^{-9} \) miles.

We know that:
\[
1 \text{ mile} = 63,360 \text{ inches}
\]

To find the distance in inches, we multiply the distance in miles by the number of inches per mile:
\[
\text{Distance in inches} = (2.37 \times 10^{-9} \text{ miles}) \times (63,360 \text{ inches/mile})
\]

Calculating this gives:
\[
2.37 \times 63,360 = 150,643.20
\]

Next, we multiply this by \( 10^{-9} \):
\[
150,643.20 \times 10^{-9}
\]

To express \( 150,643.20 \) in scientific notation, we need to write it in the form \( a \times 10^{b} \), where \( 1 \leq a < 10 \). We can move the decimal point 5 places to the left:
\[
150,643.20 = 1.5064320 \times 10^{5}
\]

Now combining this with \( 10^{-9} \):
\[
1.5064320 \times 10^{5} \times 10^{-9} = 1.5064320 \times 10^{-4}
\]

Rounding the decimal portion to the nearest hundredth gives \( 1.51 \). Hence, the final answer in scientific notation is:
\[
1.51 \times 10^{-4}
\]

Thus, the distance the tortoise traveled in inches, expressed in scientific notation and rounded to the nearest hundredth, is:
\[
\boxed{1.51 \times 10^{-4}}
\]

Answer 3

To convert \( 2.37 \times 10^{-9} \) miles to inches, we multiply by the conversion factor (63,360 inches/mile):

\[
\text{Distance in inches} = 2.37 \times 10^{-9} \times 63,360
\]

Calculating:

\[
2.37 \times 63,360 = 150,643.20
\]

Now convert to scientific notation:

\[
150,643.20 = 1.5064320 \times 10^{5}
\]

Then multiply by \( 10^{-9} \):

\[
1.5064320 \times 10^{5} \times 10^{-9} = 1.5064320 \times 10^{-4}
\]

Rounding to the nearest hundredth gives \( 1.51 \). Therefore, the final answer is:

\[
\boxed{1.51 \times 10^{-4}}
\]