Question

The distance between two cities is approximately 3.3 x 10^2. Use scientific notation to express this distance in feet if 1 mile = 5280 feet.

Answer 1

To solve the exercise, you can first convert the distance given in miles to regular notation.

Since the exponent of the scientific notation is positive, move the decimal point 2 places to the right.

Now you can use a rule of three to express the given distance in feet.

`\begin{gathered} 1\text{ mile }\rightarrow5280ft \\ 330\text{ miles }\rightarrow xft \\ x=\frac{330\text{ miles }\cdot5280\text{ ft}}{1\text{ mile}} \\ x=\frac{330\cdot5280\text{ ft}}{1} \\ x=(330\cdot5280)/(1)ft \\ x=330\cdot5280ft \\ x=1742400ft \end{gathered}`

Finally, express this distance in scientific notation. To do this, move the decimal so that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. Since the decimal is shifted to the left, the exponent will be positive.

Therefore, the distance between these two cities expressed in feet and in scientific notation is

`1.7424\cdot10^6ft`