Units of Length (Inch, Foot, Mile)
Ximena is traveling with her family on a highway in Texas when she sees a sign: "Laredo 120 miles." Her dad says they're in good shape because there are "only 120" left to go. Is that 120 kilometers? More? Less? To find out, we need to convert between two systems of measurement.
Two Systems of Length
In Mexico we measure with the International System (SI): kilometer, meter, centimeter, and millimeter. In the United States the customary system is used: inch, foot, yard, and mile. You'll see it on computer and TV screens, pipes, tires, tools, and highway signs.
Within the SI, each unit is worth 10, 100, or 1,000 times the next one:
$$1\ \text{km} = 1{,}000\ \text{m} \qquad 1\ \text{m} = 100\ \text{cm} \qquad 1\ \text{cm} = 10\ \text{mm}$$Customary units don't follow a pattern of 10. You have to learn their equivalences:
| Customary unit | Symbol | Equals |
|---|---|---|
| 1 inch | in | 2.54 cm |
| 1 foot | ft | 30.48 cm (12 in) |
| 1 yard | yd | 0.9144 m (3 ft) |
| 1 mile | mi | 1.609 km (approx.) |
A computer screen measures 24 inches. How many centimeters is that? Use $1 \text{ inch} = 2.54 \text{ cm}$.
A computer screen measures 24 inches. How many centimeters is that? Use $1 \text{ inch} = 2.54 \text{ cm}$.
Conversion Factors
An equivalence such as $1\ \text{in} = 2.54\ \text{cm}$ can be read as a ratio equal to 1:
$$\frac{2.54\ \text{cm}}{1\ \text{in}} = 1 \qquad \frac{1\ \text{in}}{2.54\ \text{cm}} = 1$$Multiplying by 1 doesn't change the measurement, only the unit it is expressed in. You choose the ratio that cancels the unit you want to get rid of.
A table is 5 feet long. Express this in centimeters and in meters. Use $1 \text{ foot} = 30.48 \text{ cm}$.
A table is 5 feet long. Express this in centimeters and in meters. Use $1 \text{ foot} = 30.48 \text{ cm}$.
A screw is 3.5 inches long. Convert it to millimeters (remember that $1 \text{ cm} = 10 \text{ mm}$).
A screw is 3.5 inches long. Convert it to millimeters (remember that $1 \text{ cm} = 10 \text{ mm}$).
Miles and Kilometers
For long distances, the United States uses the mile. We will use $1\ \text{mi} = 1.609\ \text{km}$.
To go from km to mi you divide: $100\ \text{km} \div 1.609 \approx 62.1\ \text{mi}$.
The distance between two cities is 50 miles. What is the equivalent in kilometers? Use $1 \text{ mile} = 1.609 \text{ km}$.
The distance between two cities is 50 miles. What is the equivalent in kilometers? Use $1 \text{ mile} = 1.609 \text{ km}$.
A sign on a Texas highway shows 120 miles left to reach the border. How many kilometers are left? Round to the nearest unit.
A sign on a Texas highway shows 120 miles left to reach the border. How many kilometers are left? Round to the nearest unit.
Yards and Conversion Chains
Sometimes you don't have a direct equivalence and you chain several together. Each ratio cancels one unit.
An American football field is 100 yards long. If $1 \text{ yard} = 0.9144 \text{ m}$, how many meters is that? Is it longer or shorter than a 105 m soccer field?
An American football field is 100 yards long. If $1 \text{ yard} = 0.9144 \text{ m}$, how many meters is that? Is it longer or shorter than a 105 m soccer field?
Speeds and Comparisons
A speed such as "60 miles per hour" has a unit of length on top and time on the bottom. Only the length is converted; the hours stay the same.
A car travels at 60 miles per hour on a highway in the United States. Convert that speed to kilometers per hour and decide whether it would exceed the 100 km/h limit…
A car travels at 60 miles per hour on a highway in the United States. Convert that speed to kilometers per hour and decide whether it would exceed the 100 km/h limit that applies on many Mexican highways.
The distance of a marathon is 26.2 miles. Express it in kilometers and compare it with the "official" figure of 42.195 km. Does the approximation using…
The distance of a marathon is 26.2 miles. Express it in kilometers and compare it with the "official" figure of 42.195 km. Does the approximation using $1 \text{ mile} = 1.609 \text{ km}$ come close?