Learn on PengiSaxon Algebra 1Chapter 1: Real Numbers and Basic Operations

Lesson 8: Using Unit Analysis to Convert Measures

New Concept Unit analysis is a process for converting measures into different units. A unit ratio, or conversion factor, compares 2 measures that name the same amount. What’s next This lesson builds the foundation for unit conversions. You'll work through examples involving length, area, volume, and even currency exchange rates.

Section 1

📘 Using Unit Analysis to Convert Measures

New Concept

Unit analysis is a process for converting measures into different units. A unit ratio, or conversion factor, compares 2 measures that name the same amount.

What’s next

This lesson builds the foundation for unit conversions. You'll work through examples involving length, area, volume, and even currency exchange rates.

Section 2

Unit Analysis

Property

A unit ratio, or conversion factor, compares two measures that name the same amount. Since a unit ratio is equal to 1, multiplying it by a measure changes the unit but not the amount.

Examples

Convert 5 miles to yards: 5 mi⋅1760 yd1 mi=8800 yd5 \text{ mi} \cdot \frac{1760 \text{ yd}}{1 \text{ mi}} = 8800 \text{ yd}

Convert 4000 meters to kilometers: 4000 m⋅1 km1000 m=4 km4000 \text{ m} \cdot \frac{1 \text{ km}}{1000 \text{ m}} = 4 \text{ km}

Section 3

Converting Units of Area

Property

To convert units of area, you must convert the units for both length and width. This requires multiplying by the unit ratio twice, once for each dimension. You can also square the unit ratio before multiplying.

(3 ft1 yd)2=9 ft21 yd2 \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^2 = \frac{9 \text{ ft}^2}{1 \text{ yd}^2}

Examples

Convert 10 square feet to square inches: 10 ft2⋅(12 in1 ft)2=10 ft2⋅144 in21 ft2=1440 in210 \text{ ft}^2 \cdot \left(\frac{12 \text{ in}}{1 \text{ ft}}\right)^2 = 10 \text{ ft}^2 \cdot \frac{144 \text{ in}^2}{1 \text{ ft}^2} = 1440 \text{ in}^2

Convert 5 square meters to square centimeters: 5 m2⋅(100 cm1 m)2=5 m2⋅10000 cm21 m2=50000 cm25 \text{ m}^2 \cdot \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 5 \text{ m}^2 \cdot \frac{10000 \text{ cm}^2}{1 \text{ m}^2} = 50000 \text{ cm}^2

Section 4

Converting Units of Volume

Property

To convert units of volume, you must convert the units for length, width, and height. This requires multiplying by the unit ratio three times, once for each of the three dimensions. You can also cube the unit ratio.

(1 ft12 in)3=1 ft31728 in3 \left(\frac{1 \text{ ft}}{12 \text{ in}}\right)^3 = \frac{1 \text{ ft}^3}{1728 \text{ in}^3}

Examples

Convert 3 cubic yards to cubic feet: 3 yd3⋅(3 ft1 yd)3=3 yd3⋅27 ft31 yd3=81 ft33 \text{ yd}^3 \cdot \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^3 = 3 \text{ yd}^3 \cdot \frac{27 \text{ ft}^3}{1 \text{ yd}^3} = 81 \text{ ft}^3

Convert 5000 cubic millimeters to cubic centimeters: 5000 mm3⋅(1 cm10 mm)3=5000 mm3⋅1 cm31000 mm3=5 cm35000 \text{ mm}^3 \cdot \left(\frac{1 \text{ cm}}{10 \text{ mm}}\right)^3 = 5000 \text{ mm}^3 \cdot \frac{1 \text{ cm}^3}{1000 \text{ mm}^3} = 5 \text{ cm}^3

Book overview

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Chapter 1: Real Numbers and Basic Operations

  1. Lesson 1

    Lesson 1: Classifying Real Numbers

    LearnPractice
  2. Lesson 2

    Lesson 2: Understanding Variables and Expressions

    LearnPractice
  3. Lesson 3

    Lesson 3: Simplifying Expressions Using the Product Property of Exponents

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  4. Lesson 4

    Lesson 4: Using Order of Operations

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  5. Lesson 5

    Lesson 5: Finding Absolute Value and Adding Real Numbers

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  6. Lesson 6

    Lesson 6: Subtracting Real Numbers

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  7. Lesson 7

    Lesson 7: Simplifying and Comparing Expressions with Symbols of Inclusion

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  8. Lesson 8Current

    Lesson 8: Using Unit Analysis to Convert Measures

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  9. Lesson 9

    Lesson 9: Evaluating and Comparing Algebraic Expressions

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  10. Lesson 10

    Lesson 10: Adding and Subtracting Real Numbers

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Lesson overview

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Section 1

📘 Using Unit Analysis to Convert Measures

New Concept

Unit analysis is a process for converting measures into different units. A unit ratio, or conversion factor, compares 2 measures that name the same amount.

What’s next

This lesson builds the foundation for unit conversions. You'll work through examples involving length, area, volume, and even currency exchange rates.

Section 2

Unit Analysis

Property

A unit ratio, or conversion factor, compares two measures that name the same amount. Since a unit ratio is equal to 1, multiplying it by a measure changes the unit but not the amount.

Examples

Convert 5 miles to yards: 5 mi⋅1760 yd1 mi=8800 yd5 \text{ mi} \cdot \frac{1760 \text{ yd}}{1 \text{ mi}} = 8800 \text{ yd}

Convert 4000 meters to kilometers: 4000 m⋅1 km1000 m=4 km4000 \text{ m} \cdot \frac{1 \text{ km}}{1000 \text{ m}} = 4 \text{ km}

Section 3

Converting Units of Area

Property

To convert units of area, you must convert the units for both length and width. This requires multiplying by the unit ratio twice, once for each dimension. You can also square the unit ratio before multiplying.

(3 ft1 yd)2=9 ft21 yd2 \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^2 = \frac{9 \text{ ft}^2}{1 \text{ yd}^2}

Examples

Convert 10 square feet to square inches: 10 ft2⋅(12 in1 ft)2=10 ft2⋅144 in21 ft2=1440 in210 \text{ ft}^2 \cdot \left(\frac{12 \text{ in}}{1 \text{ ft}}\right)^2 = 10 \text{ ft}^2 \cdot \frac{144 \text{ in}^2}{1 \text{ ft}^2} = 1440 \text{ in}^2

Convert 5 square meters to square centimeters: 5 m2⋅(100 cm1 m)2=5 m2⋅10000 cm21 m2=50000 cm25 \text{ m}^2 \cdot \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 5 \text{ m}^2 \cdot \frac{10000 \text{ cm}^2}{1 \text{ m}^2} = 50000 \text{ cm}^2

Section 4

Converting Units of Volume

Property

To convert units of volume, you must convert the units for length, width, and height. This requires multiplying by the unit ratio three times, once for each of the three dimensions. You can also cube the unit ratio.

(1 ft12 in)3=1 ft31728 in3 \left(\frac{1 \text{ ft}}{12 \text{ in}}\right)^3 = \frac{1 \text{ ft}^3}{1728 \text{ in}^3}

Examples

Convert 3 cubic yards to cubic feet: 3 yd3⋅(3 ft1 yd)3=3 yd3⋅27 ft31 yd3=81 ft33 \text{ yd}^3 \cdot \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^3 = 3 \text{ yd}^3 \cdot \frac{27 \text{ ft}^3}{1 \text{ yd}^3} = 81 \text{ ft}^3

Convert 5000 cubic millimeters to cubic centimeters: 5000 mm3⋅(1 cm10 mm)3=5000 mm3⋅1 cm31000 mm3=5 cm35000 \text{ mm}^3 \cdot \left(\frac{1 \text{ cm}}{10 \text{ mm}}\right)^3 = 5000 \text{ mm}^3 \cdot \frac{1 \text{ cm}^3}{1000 \text{ mm}^3} = 5 \text{ cm}^3

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Real Numbers and Basic Operations

  1. Lesson 1

    Lesson 1: Classifying Real Numbers

    LearnPractice
  2. Lesson 2

    Lesson 2: Understanding Variables and Expressions

    LearnPractice
  3. Lesson 3

    Lesson 3: Simplifying Expressions Using the Product Property of Exponents

    LearnPractice
  4. Lesson 4

    Lesson 4: Using Order of Operations

    LearnPractice
  5. Lesson 5

    Lesson 5: Finding Absolute Value and Adding Real Numbers

    LearnPractice
  6. Lesson 6

    Lesson 6: Subtracting Real Numbers

    LearnPractice
  7. Lesson 7

    Lesson 7: Simplifying and Comparing Expressions with Symbols of Inclusion

    LearnPractice
  8. Lesson 8Current

    Lesson 8: Using Unit Analysis to Convert Measures

    LearnPractice
  9. Lesson 9

    Lesson 9: Evaluating and Comparing Algebraic Expressions

    LearnPractice
  10. Lesson 10

    Lesson 10: Adding and Subtracting Real Numbers

    LearnPractice