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

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

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

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

6. Solution
A. 1 kg = ____ g
3) 1000 g
B. 1 mm = ____ m
1) 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 = 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. Conversion factors 100 cm 1 m = 100 cm 1 m = = 1 100 cm
Can divide each side by 100 cm to
equal 1
100 cm
1 m = = 1
100 cm

13. Conversion factors
1 m 1 =
100 cm

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

15. Conversion factors
1 m 1 =
100 cm 1
100 cm =
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 A. Liters and mL B. Hours and minutes
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 hr = 60 min
1 hr and min
60 min hr
C. meters and kilometers 1 km = 1000 m
1 km and m
1000 m km

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