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Lesson 4.3.1

Customary and Metric Units. Lesson 4.3.1. Lesson 4.3.1. Customary and Metric Units. California Standards: Algebra and Functions 2.1 Convert one unit of measurement to another (for example, from feet to miles, from centimeters to inches). Mathematical Reasoning 3.1

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Lesson 4.3.1

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  1. Customary and Metric Units Lesson 4.3.1

  2. Lesson 4.3.1 Customary and Metric Units California Standards: Algebra and Functions 2.1 Convert one unit of measurement to another(for example, from feet to miles, from centimeters to inches). Mathematical Reasoning 3.1 Evaluate the reasonableness of the solution in the context of the original situation. What it means for you: You’ll see how to convert between different units within the customary or metric systems. For example, feet to inches, or meters to kilometers. • Key words: • conversion • customary system • metric system • unit • conversion table • conversion factor

  3. Lesson 4.3.1 Customary and Metric Units This Lesson, you’ll learn how to convert between units in either the customary or the metric system. So you take a length in inches, say, and convert it to feet. Or maybe you know a length in centimeters and you need to convert it to kilometers. That kind of thing…

  4. Customary lengths 1 foot (ft) = 12 inches (in.) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 1760 yards (yd) Lesson 4.3.1 Customary and Metric Units Customary Lengths Are Inches, Feet, Yards, and Miles The customary system of lengths is the system that uses inches, feet, yards, and miles. This conversion table shows how many of one unit make up another kind of unit. You can use it to convert a measurement in one unit to a measurement in another unit. The numbers in a conversion table (12, 3, and 1760 in the above table) are sometimes called conversion factors.

  5. Customary lengths 1 foot (ft) = 12 inches (in.) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 1760 yards (yd) Lesson 4.3.1 Customary and Metric Units Example 1 A vase is 1 yard tall. What is its height in: (i) feet? (ii) inches? Solution (i) Using the conversion table,you can see that 1 yard is 3 feet. (ii) If 1 foot is 12 inches, then 3 feet must be 3 × 12 = 36 inches. Solution follows…

  6. Lesson 4.3.1 Customary and Metric Units Notice that when you convert to a smaller unit, the number gets bigger. This makes sense… the smaller each unit, the more of them you need to cover the same distance. In fact, if your conversion factor is greater than 1: ● you multiply by it to convert to a smaller unit, since this gives you a bigger number. ● you divide by it to convert to a bigger unit, since this gives you a smaller number.

  7. Customary lengths 1 foot (ft) = 12 inches (in.) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 1760 yards (yd) Lesson 4.3.1 Customary and Metric Units Example 2 Convert: (i) 3 miles to yards, (ii) 7920 yards to miles. Solution There are 1760 yards in a mile, so use 1760 as your conversion factor. (i) Yards are smaller than miles, so 3 miles = 3 × 1760 = 5280 yd. (ii) Miles are bigger than yards: 7920 yd = 7920 ÷ 1760 = 4.5 miles. Solution follows…

  8. × 12 × 3 ÷ 12 × 1760 ÷ 3 ÷ 1760 Lesson 4.3.1 Customary and Metric Units This diagram summarizes how to convert between customary lengths. To get from miles to inches, first × by 1760, then × by 3, then × by 12. To get from inches to miles, first ÷ by 12, then ÷ by 3, then ÷ by 1760.

  9. Lesson 4.3.1 Customary and Metric Units Guided Practice Convert: 1. 7 miles to yards 2. 8800 yards to miles 3. 72 inches to feet 4. 12 feet to yards 5. 5 feet to inches 6. 9 yards to inches 7. 1 mile to feet 8. 8 yards to inches 7 × 1760 = 12,320 yd 8800 ÷ 1760 = 5 mi 72 ÷ 12 = 6 ft 12 ÷ 3 = 4 yd 5 × 12 = 60 in. 9 × 3 = 27 ft 27 × 12 = 324 in. 1 × 1760 = 1760 yd 1760 × 3 = 5280 ft 8 × 3 = 24 ft 24 × 12 = 288 in. Solution follows…

  10. 7 1 1 1 7 1 3 3 3 9 9 3 Lesson 4.3.1 Customary and Metric Units Guided Practice Convert: 9. 2 miles to inches 10. 100,000 inches to miles 2 × 1760 = 3520 yd 3520 × 3 = 10,560 ft 10,560 × 12 = 126,720 in. 100,000 ÷ 12 = 8333 8333 ÷ 3 = 2777 2777 ÷ 1760 = 1.5783 mi 11. If Letitia cycles 3 miles, how many feet has she gone? 3 × 1760 = 5280 yd 5280 × 3 = 15,840 ft 12. Mount Whitney is 14,494 feet tall. How many miles is this? 14,494 ÷ 3 = 4831 yd 4831 ÷ 1760 = 2.745 mi Solution follows…

  11. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units The Metric System Is Based on the Meter The metric system of lengths is based on the meter. All metric units for length contain the word “meter” — millimeter, centimeter, decimeter… Here’s a conversion table. These are all bigger than meters. These are all smaller than meters. Notice that some of the conversion factors are less than one.

  12. Lesson 4.3.1 Customary and Metric Units Example 3 Convert 120 meters to millimeters. Solution You’re converting from a big unit (meters) to a smaller one (millimeters), so the number needs to be bigger. The conversion factor is 0.001 (1 mm = 0.001 m). This is less than 1, so to make a bigger number, you need to divide by the conversion factor. 120 m = 120 ÷ 0.001 = 120 × 1000 = 120,000 mm Solution follows…

  13. Lesson 4.3.1 Customary and Metric Units Example 4 A pencil is 10 cm long. How long is the pencil in kilometers? Solution First, convert 10 cm to meters by multiplying by 0.01. This gives a smaller number: 10 centimeters = 10 × 0.01 = 0.1 m Next, convert 0.1 m to kilometers by dividing by 1000. This also gives a smaller number: 0.1 m = 0.1 ÷ 1000 = 0.0001 km Solution follows…

  14. × 10 × 10 ÷ 10 × 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 × 10 × 10 × 10 Lesson 4.3.1 Customary and Metric Units This diagram summarizes how to convert between metric lengths. Multiply by 10 to convert one step smaller. Multiply by 100 to convert two steps smaller, etc… Divide by 10 to convert one step bigger. Divide by 100 to convert two steps bigger, etc…

  15. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Guided Practice Convert: 13. 7 km to m 14. 8700 m to km 15. 85 mm to cm 16. 120 cm to mm 17. 180 m to km 18. 15,000 m to km 7 × 1000 = 7000 m 8700 ÷ 1000 = 8.7 km 85 ÷ 10 = 8.5 cm 120 × 10 = 1200 mm 180 ÷ 1000 = 0.18 km 15,000 ÷ 1000 = 15 km Solution follows…

  16. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Guided Practice Convert: 19. 0.1 km to m 20. 160 mm to cm 0.1 × 1000 = 100 m 160 ÷ 10 = 16 cm 21. A snail moves 3 m. How many cm is this? 3 × 100 = 300 cm Solution follows…

  17. Lesson 4.3.1 Customary and Metric Units Independent Practice There are 12 inches in 1 foot, meaning the conversion factor is 12. 1. Would you divide by 12 or multiply by 12 when converting from feet to inches? Multiply 2. Would you divide by 12 or multiply by 12 when converting from inches to feet? Divide Solution follows…

  18. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice 3. How would you convert from yards to miles? Divide by 1760 In Exercises 4–9, find the missing values in the conversions. 4. 36 in. = ? yd 5. 144 in. = ? yd 6. 27 ft = ? yd 7. 100 yd = ? ft 8. 99 ft = ? yd 9. 0.25 mi = ? ft 1 4 9 300 33 1320 Solution follows…

  19. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice 10. TJ’s guitar is 3.5 ft long. What is the length of the guitar in inches? 42 in. 11. Would you divide by 100 or multiply by 100 when converting from meters to centimeters? Multiply by 100 Solution follows…

  20. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice 12. There are 1000 millimeters in a meter, and 100 meters in a hectometer. What is the conversion factor when converting millimeters to hectometers? 100,000 (or 0.00001) 13. Would you multiply or divide by this conversion factor when converting millimeters to hectometers? Divide by 100,000 (but multiply by 0.00001) Solution follows…

  21. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice Find the missing value in Exercises 14–19. 14. 30 m = ? cm 15. 2 km = ? m 16. 250 mm = ? cm 17. 0.5 cm = ? m 18. 4 dam = ? dm 19. 0.37 dm = ? mm 2000 3000 25 0.005 400 37 Solution follows…

  22. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice 20. An Olympic swimming pool has a length of 50 meters. What is this distance in kilometers? 0.05 km The length of the wingspan of an airplane is 40 m. 21. Find the wingspan of this airplane in centimeters. 4000 cm 22. Find the wingspan of this airplane in kilometers. 0.04 km Solution follows…

  23. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice A compact disc has a diameter of 120 millimeters. 23. What is the diameter of a compact disc in centimeters? 12 cm 24. What is the diameter of a compact disc in decimeters? 1.2 dm 25. Ying and Carol jog exactly 2 miles together every Saturday. They both guess how many inches their jog is. Ying guessed 100,000 in. and Carol guessed 10,000 in. Whose guess is closer to the actual amount? Ying’s (the actual number is 126,720) Solution follows…

  24. Metric lengths 1 decimeter (dm) = 0.1 meters 1 dekameter (dam) = 10 meters 1 centimeter (cm) = 0.01 meters 1 hectometer (hm) = 100 meters 1 millimeter (mm) = 0.001 meters 1 kilometer (km) = 1000 meters Lesson 4.3.1 Customary and Metric Units Independent Practice Micrometers are metric units that can be used to measure very small objects. In fact, 1 millimeter is equal to 1000 micrometers. 26. How many micrometers are in 0.25 millimeters? 250 micrometers 27. How many micrometers are in 1 kilometer? 1,000,000,000 (1 billion) micrometers Solution follows…

  25. Lesson 4.3.1 Customary and Metric Units Round Up So to convert something from one unit to another, you need to make the number either bigger(if you’re converting to a smaller unit) or smaller(if you’re converting to a bigger unit). Conversion factors are useful, but you have to use them sensibly. There’s more on conversions next Lesson.

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