\[
1 \text{ kilometer } (km) = 1000 \text{ meters } (m)
\]
\[
1 \text{ meter } (m) = 100 \text{ centimeters } (cm)
\]
\[
1 \text{ centimeter } (cm) = 10^{-2} \text{ meters } (m)
\]
\[
1 \text{ millimeter } (mm) = 10^{-3} \text{ meters } (m)
\]
\[
1 \text{ inch } (in) = 2.540 \text{ cm}
\]
\[
1 \text{ foot } (ft) = 30.48 \text{ cm}
\]
\[
1 \text{ mile } (mi) = 1.609 \text{ kilometers } (km)
\]
Worked Example:
Convert \( 5000 \text{ inches} \) into meters.
Step 1: Convert inches to centimeters:
\[
5000 \text{ in} \times 2.54 \text{ cm/in} = 12,700 \text{ cm}
\]
Step 2: Convert centimeters to meters:
\[
12,700 \text{ cm} \times 10^{-2} \text{ m/cm} = 127 \text{ m}
\]
Solution:
\( 5000 \text{ inches} = 127 \text{ meters} \)
\[
1 \text{ square meter } (m^2) = 10.76 \text{ square feet } (ft^2)
\]
\[
1 \text{ square foot } (ft^2) = 929 \text{ square centimeters } (cm^2)
\]
\[
1 \text{ acre } = 43,560 \text{ square feet } (ft^2)
\]
Worked Example:
Convert \( 2 \text{ acres} \) into square meters.
Step 1: Convert acres to square feet:
\[
2 \text{ acres} \times 43,560 \text{ ft}^2/\text{acre} = 87,120 \text{ ft}^2
\]
Step 2: Convert square feet to square meters:
\[
87,120 \text{ ft}^2 \times \frac{1 \text{ m}^2}{10.76 \text{ ft}^2} = 8,096.87 \text{ m}^2
\]
Solution:
\( 2 \text{ acres} = 8,096.87 \text{ square meters} \)
\[
1 \text{ liter } (l) = 1000 \text{ cm}^3 = 0.03532 \text{ ft}^3
\]
\[
1 \text{ cubic meter } (m^3) = 35.32 \text{ ft}^3
\]
\[
1 \text{ U.S. gallon } (gal) = 3.785 \text{ liters} (l)
\]
Worked Example:
Convert \( 3 \text{ cubic meters} \) into liters.
Step 1: Convert cubic meters to liters:
\[
3 \text{ m}^3 \times 1000 \text{ l/m}^3 = 3000 \text{ liters}
\]
Solution:
\( 3 \text{ cubic meters} = 3000 \text{ liters} \)
\[
1 \text{ kilogram } (kg) = 2.2046 \text{ pounds } (lb)
\]
\[
1 \text{ pound } (lb) = 453.6 \text{ grams } (g)
\]
\[
1 \text{ slug } = 32.174 \text{ pounds } (lb)
\]
Worked Example:
Convert \( 150 \text{ pounds} \) into kilograms.
Step 1: Convert pounds to kilograms:
\[
150 \text{ lb} \times \frac{1 \text{ kg}}{2.2046 \text{ lb}} = 68.04 \text{ kg}
\]
Solution:
\( 150 \text{ pounds} = 68.04 \text{ kilograms} \)
\[
1 \text{ kilometer per hour } (km/h) = 0.6214 \text{ miles per hour } (mi/h)
\]
\[
1 \text{ mile per hour } (mi/h) = 1.609 \text{ kilometers per hour } (km/h)
\]
Worked Example:
Convert \( 100 \text{ miles per hour} \) into kilometers per hour.
Step 1: Convert miles per hour to kilometers per hour:
\[
100 \text{ mi/h} \times 1.609 \text{ km/mi} = 160.9 \text{ km/h}
\]
Solution:
\( 100 \text{ miles per hour} = 160.9 \text{ kilometers per hour} \)
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Common Conversion Methods:
1. Multiplication by Conversion Factors:
– To convert units, multiply the original measurement by a conversion factor, which is a ratio that expresses how many of one unit are equal to another unit.
– For example, to convert 10 miles to kilometers, use the conversion factor \(1 \, \text{mile} = 1.60934 \, \text{km}\):
\[
10 \, \text{miles} \times 1.60934 \, \frac{\text{km}}{\text{mile}} = 16.0934 \, \text{km}
\]
2. Dimensional Analysis (Factor-Label Method):
– This method involves multiplying the quantity by one or more conversion factors such that units cancel appropriately, leaving the desired unit.
– Example: Convert 5 meters per second to kilometers per hour.
\[
5 \, \frac{\text{m}}{\text{s}} \times \frac{1 \, \text{km}}{1000 \, \text{m}} \times \frac{3600 \, \text{s}}{1 \, \text{hour}} = 18 \, \frac{\text{km}}{\text{hour}}
\]
Common Unit Conversions:
– Length:
– 1 inch = 2.54 cm
– 1 foot = 0.3048 meters
– 1 mile = 1.60934 kilometers
– Mass:
– 1 pound (lb) = 0.453592 kilograms (kg)
– 1 ounce = 28.3495 grams (g)
– 1 ton = 907.185 kilograms
– Volume:
– 1 gallon (US) = 3.78541 liters
– 1 liter = 1000 milliliters (ml)
– 1 cubic foot = 28.3168 liters
– Time:
– 1 hour = 3600 seconds
– 1 day = 24 hours
– 1 year = 365.25 days
– Temperature:
– Fahrenheit to Celsius: \((°F – 32) \times \frac{5}{9} = °C\)
– Celsius to Fahrenheit: \((°C \times \frac{9}{5}) + 32 = °F\)
– Celsius to Kelvin: \(°C + 273.15 = K\)
– Energy:
– 1 calorie (cal) = 4.184 joules (J)
– 1 kilowatt-hour (kWh) = 3.6 × 10^6 joules
– Speed:
– 1 meter per second (m/s) = 3.6 kilometers per hour (km/h)
– 1 mile per hour (mph) = 1.60934 km/h
Conversion Tools:
Online converters and calculators can also be useful for quickly converting units without manual calculations. Examples include Google’s built-in converter or dedicated conversion tools like [UnitConverter](https://www.unitconverters.net/) for various unit conversions.
Understanding these conversion methods and memorizing key conversion factors can help you tackle unit conversion problems efficiently in any field.