Exercise 3 Page 2

To convert the length from miles to kilometers, we will have to convert from imperial units to metric units. One possible conversion rate is that 1 in. corresponds to 2.54 cm. Therefore, our first step is to convert 120 miles to inches. We will start with the information that 1 mile is equivalent to 5280 feet. \dfrac{5280\text{ ft}}{1\cancel\text{ mile}}\cdot120\cancel\text{ miles}=633\,600 \text{ ft} This means that 120 miles corresponds to 633 600 feet. Since one foot is equivalent to 12 inches, if we multiply our length by 12 we will get the distance in inches.

\dfrac{12\text{ in}}{1\cancel\text{ ft}}\cdot633\,600\cancel\text{ ft}=7\,603\,200\text{ in} Now that we have our length in inches, and can use the conversion to centimeters, we will multiply our length by 2.54. \dfrac{2.54\text{ cm}}{1\cancel\text{ in}}\cdot7\,603\,200\cancel\text{ in}=19\,312\,128 After the calculation, we know that 120 miles corresponds to 19 312 128 centimeters. Our last step is to convert the length to kilometers. We will have to know how many centimeters are in 1 kilometer. We need to use the fact that 1 kilometer is 1000 meters and 1 meter is 100 centimeters. \dfrac{1000\cancel\text{ m}}{1\text{ km}}\cdot\dfrac{100\text{ cm}}{1\cancel\text{ m}}=\dfrac{100\,000\text{ cm}}{1\text{ km}} Therefore, 1 kilometer is equivalent to 100 000 centimeters. To get our distance in kilometers, we will have to divide the length with 100 000. \dfrac{1\text{ km}}{100\,000\cancel\text{ cm}}\cdot 19\,312\,128\cancel\text{ cm}=193.12128\text{ km} As the answer should be a whole number, the distance in kilometers would be 193 kilometers.

Hints

Check the answer