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