Mathematics
Grade 10
15 min
Convert between metric and customary units
Convert between metric and customary units
What you'll learn
- Identify the correct conversion factor (e.g., 1 inch = 2.54 centimeters) for converting between common metric and customary units of length, weight/mass, and volume with 80% accuracy on a worksheet.
- Solve word problems involving conversion between metric and customary units of length, weight/mass, and volume using multiplication or division, showing their work, and achieving at least 70% accuracy on a quiz.
- Explain the process of converting a measurement from one unit (e.g., inches) to another unit (e.g., centimeters) in a complete sentence, demonstrating understanding of the relationship between the units.
- Apply conversion skills to estimate the equivalent customary measurement for a metric measurement (or vice versa) of objects in the classroom with reasonable accuracy (within 20% of the actual conversion).
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the necessary conversion factor to switch between a given metric and customary unit of length.
Convert a side length of a right triangle from a metric unit (e.g., meters, centimeters) to a customary unit (e.g., feet, inches).
Convert a side length of a right triangle from a customary unit to a metric unit.
Apply the Pythagorean theorem to right triangles with side lengths given in mixed unit systems by first converting them to a single system.
Solve trigonometric problems (sine, cosine, tangent) involving right triangles where the final answer requires a unit conversion.
Analyze and solve real-world word problems involving right triangles that require conversions between metric and customary units.
Ever wonder how an American architect (using fee...
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Key Concepts & Vocabulary
TermDefinitionExample
Metric SystemA decimal-based system of measurement used by most of the world, based on units like the meter, liter, and gram.The height of a standard door is about 2 meters.
Customary System (U.S.)The system of measurement primarily used in the United States, including units like feet, inches, pounds, and gallons.The same door is about 6 feet 7 inches tall.
Conversion FactorA ratio or fraction which represents the relationship between two different units and is equal to 1.The ratio `(2.54 cm / 1 inch)` is a conversion factor used to change inches to centimeters.
Dimensional AnalysisA problem-solving method that uses conversion factors to change units. Units are treated like algebraic variables that can be cancelled out.To convert 5 inches to cm, you calculate `5 \tex...
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Core Formulas
Length Conversion: Inches to Centimeters (Exact)
1 \text{ inch} = 2.54 \text{ centimeters}
This is the fundamental, exact conversion factor for length. Use it to convert inches to centimeters by multiplying by 2.54, or centimeters to inches by dividing by 2.54.
Length Conversion: Feet to Meters (Approximate)
1 \text{ meter} \approx 3.281 \text{ feet}
A common and useful approximation for larger distances. To convert meters to feet, multiply by 3.281. To convert feet to meters, divide by 3.281.
The Conversion Process (Dimensional Analysis)
\text{Given Quantity} \times \frac{\text{Desired Unit}}{\text{Given Unit}} = \text{Result in Desired Unit}
To convert a measurement, multiply it by a conversion factor (a fraction equal to 1) where the unit you want to cancel out is...
4 more steps in this tutorial
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Challenging
The legs of a right triangle measure 8 feet and 1.5 meters. What is the sine of the angle opposite the 8-foot leg, rounded to three decimal places?
A.0.625
B.0.852
C.0.514
D.0.932
Challenging
From a point on the ground, the angle of elevation to the top of a tree is 60°. The point is 10 meters from the base of the tree. A bird is perched on top of the tree. How high is the bird off the ground, in feet, rounded to the nearest foot?
A.57 feet
B.33 feet
C.17 feet
D.50 feet
Challenging
Two vertical poles stand on level ground. One is 10 meters tall and the other is 32 feet tall. A wire connects the tops of the poles. Which statement is the most accurate description of the length difference?
A.The 10-meter pole is taller by about 10 inches.
B.The 32-foot pole is taller by about 2 feet.
C.The 10-meter pole is taller by about 2.8 feet.
D.The 10-meter pole is taller by about 10 centimeters.
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Frequently asked questions
What grade level is "Convert between metric and customary units"?
Convert between metric and customary units is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Convert between metric and customary units?
You'll be able to: Identify the correct conversion factor (e.g., 1 inch = 2.54 centimeters) for converting between common metric and customary units of length, weight/mass, and volume with 80% accuracy on a worksheet; Solve word problems involving….
Is "Convert between metric and customary units" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Convert between metric and customary units?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.