Equalities

1. Equalities State the same measurement in two different units length 10.0 in. 254 mm

2. Some Metric Equalities Length 1 m = 100 cm Mass 1 kg = 1000 g Volume 1 L = 1000 mL

3. Learning Check A. 1000 m = 1 ___1) mm 2) km 3) dm B. 0.001 g = 1 ___1) mg 2) kg 3) dg C. 0.1 L = 1 ___1) mL 2) cL 3) dL D. 0.01 m = 1 ___1) mm 2) cm 3) dm

4. Solution A. 1000 m = 1 ___ 2) km B. 0.001 g = 1 ___ 1) mg C. 0.1 L = 1 ___ 3) dL D. 0.01 m = 1 ___ 2) cm

5. Learning Check Give the value of the following units: A. 1 kg = ____ g 1) 10 g 2) 100 g 3) 1000 g B. 1 mm = ____ m 1) 0.001 m 2) 0.01 m 3) 0.1 m

6. Solution A. 1 kg = ____ g 3) 1000 g B. 1 mm = ____ m 1) 0.001 m

7. Some American Equalities 1 ft = inches 1 lb = 16 oz 1 quart = pints 1 quart = 4 cups Why are the quantities in each pair equal?

8. Some American Equalities 1 ft = 12 inches 1 lb = 16 oz 1 quart = 2 pints 1 quart = 4 cups The quantities in each pair give the same measured amount in two different units.

9. Some Metric-American Equalities 1 in. = 2.54 cm 1 qt = 946 mL 1 L = 1.06 qt 1 lb = 454 g 1 kg = 2.20 lb

10. Equalities given in a Problem Example 1 At the store, the price of one pound of red peppers is $2.39. Equality: 1 lb red peppers = $2.39 Example 2 At the gas station, one gallon of gas is $1.34. Equality: 1 gallon of gas = $1.34

11. Conversion factors • “A ratio of equalities or equivalent measurements.” • Start with two quantities that are the same. One meter is one hundred centimeters • Write it as an equation. 1 m = 100 cm • Can divide each side by either quantity to equal 1.

12. 1 m 1 m 100 cm 100 cm 100 cm 100 cm Conversion factors = Can divide each side by 100 cm to equal 1 = = 1

13. Conversion factors 1 m 1 = 100 cm

14. 1 m = 100 cm 1 m 1 m Conversion factors 1 m 1 = 100 cm 1 =

15. Conversion factors 1 m 1 = 100 cm 100 cm 1 = 1 m

16. Conversion factors • Called conversion factors because they allow us to convert units. • Really just multiplying quantities by 1. • Exact quantities so they have unlimited significant figures. • Equivalence statements always have this relationship. big # small unit = small # big unit 1000 mm = 1 m

17. Learning Check Write conversion factors that relate each of the following pairs of units: A. Liters and mL B. Hours and minutes D. Meters and kilometers

18. Solution A. liters and mL 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L B. hours and minutes 1 hr = 60 min 1 hr and 60 min 60 min 1 hr C. meters and kilometers 1 km = 1000 m 1 km and 1000 m 1000 m 1 km

19. Write the conversion factors for the following • kilograms to grams • feet to inches • 1.096 qt. = 1.00 L