Mathematics
Grade 10
15 min
Convert rates and measurements: metric units
Convert rates and measurements: metric units
What you'll learn
- Identify the variables and constants in word problems with at least 80% accuracy.
- Translate at least 3 out of 4 word problems into correct variable expressions using appropriate operations (+, -, x, /).
- Explain in their own words how a variable represents an unknown number in a word problem, providing at least two different examples.
- Solve for the variable in a simple one-step equation derived from a word problem, achieving a minimum of 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert single metric units of length, mass, and volume.
Convert squared and cubed metric units for area and volume (e.g., cm² to m², mm³ to cm³).
Convert compound rates involving metric units (e.g., m/s to km/h).
Apply metric conversions to solve problems involving the surface area and volume of 3D figures.
Analyze and solve multi-step word problems requiring unit conversions.
Use scientific notation to represent and convert very large or very small metric measurements.
Ever wonder how an Olympic sprinter's speed of 10 meters per second translates to kilometers per hour? 🏃♀️💨 This lesson shows you how to make that conversion and many more!
This tutorial will master the art of converting metric units, from simple lengths to complex rates like den...
2
Key Concepts & Vocabulary
TermDefinitionExample
Base UnitThe fundamental unit in a system of measurement. In the metric system, base units include the meter (m) for length, gram (g) for mass, and liter (L) for volume.The meter (m) is the base unit for length.
Metric PrefixA prefix attached to a base unit to indicate a multiple or fraction of that unit, based on powers of 10.The prefix 'kilo-' means 1000, so 1 kilometer (km) is 1000 meters.
Conversion FactorA ratio or fraction which represents the relationship between two different units and is equal to 1.To convert meters to centimeters, the conversion factor is (100 cm / 1 m).
RateA ratio that compares two quantities measured in different units.Speed is a rate, such as 90 kilometers per hour (90 km/h).
Dimensional AnalysisA problem-solving method that u...
3
Core Formulas
Single Unit Conversion
Final Value = Initial Value × (New Unit / Old Unit)
To convert a single unit, multiply the initial value by a conversion factor. The unit you are converting FROM (Old Unit) must be in the denominator to cancel it out.
Squared Unit Conversion (Area)
1\ m^2 = (100\ cm)^2 = 10,000\ cm^2
When converting squared units for area, you must square the entire conversion factor for the corresponding linear units. For example, since 1 m = 100 cm, the area conversion factor is (100 cm / 1 m)², which equals 10,000 cm²/m².
Cubed Unit Conversion (Volume)
1\ m^3 = (100\ cm)^3 = 1,000,000\ cm^3
When converting cubed units for volume, you must cube the entire conversion factor for the corresponding linear units. Since 1 m = 100 cm, the volume conversion factor is...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
An irregularly shaped rock has a mass of 2.16 kg. When submerged in water, it displaces 800 cm³ of water. What is the density of the rock in g/cm³?
A.0.0027 g/cm³
B.2.7 g/cm³
C.27 g/cm³
D.370 g/cm³
Challenging
Water flows into a large cubic tank with side lengths of 3 meters at a rate of 25 Liters per second. How many minutes will it take to fill the tank completely?
A.18 minutes
B.1080 minutes
C.1.8 minutes
D.11.1 minutes
Challenging
A material's heat transfer coefficient is 1500 W/(m²·K). To model a microchip, this value must be converted to W/(cm²·K). What is the correct converted value?
A.15 W/(cm²·K)
B.1.5 W/(cm²·K)
C.0.15 W/(cm²·K)
D.0.015 W/(cm²·K)
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Measurement
Mathematics for other grades
Frequently asked questions
What grade level is "Convert rates and measurements: metric units"?
Convert rates and measurements: metric units is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Convert rates and measurements: metric units?
You'll be able to: Identify the variables and constants in word problems with at least 80% accuracy; Translate at least 3 out of 4 word problems into correct variable expressions using appropriate operations (+, -, x, /); Explain in their own….
Is "Convert rates and measurements: metric 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 rates and measurements: metric units?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.