Lesson 7: Converting Measures

Property

When converting measurements, units define the meaning and scale of quantities.
The same numerical value can represent vastly different amounts depending on its units.
To convert between units, we must understand the relationship between the original and target units, ensuring the converted value maintains the same physical quantity.

Examples

Property

Key cross-system conversion factors: $1 \text{ in.} \approx 2.54 \text{ cm}$, $1 \text{ mi} \approx 1.61 \text{ km}$, and $1 \text{ m} \approx 3.28 \text{ ft}$

Examples

Property

Use ratio reasoning to convert measurement units. Recognizing the relationship between units helps determine if the answer is reasonable.

• When converting from a larger unit to a smaller unit (e.g., feet to inches), the resulting number will be larger.
• When converting from a smaller unit to a larger unit (e.g., centimeters to meters), the resulting number will be smaller.

Examples

• To convert 5 feet to inches, you multiply because you are going from a larger unit to a smaller one. Since 1 foot = 12 inches, $5 \times 12 = 60$ inches.
• To convert 350 centimeters to meters, you divide because you are going from a smaller unit to a larger one. Since 1 meter = 100 cm, $350 \div 100 = 3.5$ meters.
• A recipe requires 4 quarts of broth. How many pints is that? Since 1 quart = 2 pints (a smaller unit), we multiply: $4 \times 2 = 8$ pints.

Explanation

Converting units is like trading money. If you trade large bills (like gallons) for small coins (like pints), you get many more coins. If you trade small units (like inches) for large ones (like feet), you get fewer large units.