Conversion Problems What strategies can I use to solve problems in Science?

1. Conversion ProblemsWhat strategies can I use to solve problems in Science? • A conversion factor is a ratio of equivalent measurements used to convert between units • Measurement in numerator = measurement in denominator • For example: 1m/100cm 1m = 100cm • When a measurement is multiplied by a conversion factor, the numerical value changes, but the actual size does not. Why?

2. Conversion factors • A unique way of writing the number 1. • In the same system they are defined quantities so they have unlimited significant figures. • Equivalence statements always have this relationship. • big # small unit = small # big unit • 1000 mm = 1 m

3. Conversion Factors • How do we decide what goes on top and what goes on the bottom? • Generally, the units we want to convert TO: go on the top. The units we are converting FROM: go on the bottom. (SEE YOUR GIFT LABEL!) • This ensures that the units we were given cancel • Units must be on opposite sides of the fraction in order to cancel. Think John Travolta in Saturday Night Fever….

4. Conversion Factors • For example: Convert 750dg to grams. • First write down what you are given • Then construct a conversion factor that causes your given units to cancel • 750dg │ 1g = 75g │10dg • Where can we find the numbers we need? • Your reference tables • Write conversion factors for: nm to m and m to nm µL to L and L to µL

5. Dimensional Analysis • A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) • in meters? • A race is 10.0 km long. How far is this in miles? • 1 mile = 1760 yds • 1 meter = 1.094 yds • Pikes peak is 14,110 ft above sea level. What is this in meters?

6. 1 m 1 m 1 m 1 m 100 cm 100 cm 100 cm 100 cm 3 Units to a Power • How many m3 is 1500 cm3? 1500 cm3 1500 cm3

7. Units to a Power • How many cm2 is 15 m2? • 36 cm3 is how many mm3?

8. Converting Between Units • Dimensional Analysis - A way to analyze and solve problems using the units, or dimensions of the measurements • When converting between units it is often necessary to use more than one conversion factor. • First convert from your given value to the base unit. Convert from the base unit to your unknown value. • For example: What is 0.073cm in micrometers? • 0.073cm │ 1m │106µm = 730µm │100cm│ 1m

9. Questions to Ponder • Convert the following: • 36cm to meters • 3.72x10-3kg to grams • 66.3L to cubic centimeter • Convert the following: 4. 7.5x104nm to kilometers 5. 3.9x105mg to decigrams 6. 2.21x10-4dL to microliters

10. Answers! • 0.36m • 3.72g • 6.63x104cm3 • 7.5x10-8km • 3.9x103dg • 22.1µL

11. More Complex Units • When you are given a measurement expressed as a ration of two units, such as density or speed, multiple steps are needed. • Convert one unit at a time! • You must cube the conversion when converting a cubed unit • For example: The density of manganese is 7.21g/cm3. What is the density of manganese expressed in units of kg/m3? • Our gift label is upside down when converting the unit in the denominator of a fraction. • 7.21g │ 1kg │ (100cm)3 = 7.21x103kg/m3 1cm3│1000g│ (1m)3

12. A European cheese making recipe calls for 2.50 kg of whole milk. An American wishes to make the recipe has only measuring cups, which are marked in cups. If the density of milk is 1.03 g/cm3 how many cups of milk does he need? 1 gal = 4 qt 1 L = 1.06 qt 1 lb = 454 g 1 mi =1760 yds 1 pint = 2 cups 1 qt = 2 pints 1 yd = 3 ft. 1 mile = 1.61 km 1 m = 1.094 yds 1 L = 1000 cm3

13. More Questions to Ponder • Light travels at a speed of 3.00x1010cm/s. What is the speed of light in kilometers per hour? • A bar of gold measures 4.5cm by 6.5cm by 1.6dm. Calculate the mass of the gold bar in kilograms. The density of gold is 19.3g/cm3 • What is the mass in kilograms, of 14.0L of gasoline? (assume that the density of gasoline is 0.680g/cm3)

14. Answers! • 1.08x109km/hr • 9.0kg • 9.52kg