Metric Prefixes, Conversions and Introduction to Dimensional Analysis

1. Metric Prefixes, Conversions and Introduction to Dimensional Analysis

2. Unit : A standard quantity against which a quantity is measured [e.g. gram, metre, second, Quantity : A property that is measured [e.g. mass, length, time, volume, pressure]. Unit : A standard quantity against which a quantity is measured [e.g. gram, meter, second, liter, Pascal; which are units of the above quantities]. International System of Units (SI units) : The internationally adopted system which defines or expresses all quantities in terms of seven basic units. We cover five: Quantity : A property that is measured [e.g. mass, length, time, volume, pressure]. litre, pascal; which are units of the above quantities].

3. Measurement Base Unit(abbreviation) • Mass gram (g) • Distance meter (m) • Time second (s) • Volume liter (L) • Quantity mole (mol)

4. 1 m = 100 cm = 1 x 102 cm = 102 cm • 1 m =1,000 mm = 1 x 103 mm = 103 mm • 1m =1,000,000 mm = 1 x 106 mm = 106 µm • 1m = 1,000,000,000 nm = 1 x 109 nm = 109 nm • 1m = 1,000,000,000,000 pm= 1 x 1012 pm= 1012 pm • 1 km = 1,000 m = 1 x 103 m = 103 m

5. It is important that you memorize at least the following conversions, and always to their base unit. • ConversionExample • Kilo to base (g) 1 kg = 103 g • Base to centi (g) 1 g = 102 cg • Base to milli (L) 1 L = 103 mL • Base to micro (m) 1 m = 106 mm • Base to nano (s) 1 s = 109 ns

6. We will use these equalities to set up proportions equal to 1. • For example: 1 km = 103 m • If you divide both sides by 1 km you get: • 1 km = 1 = 103m or 1 km = 103 m = 1 • 1 km 1 km 103 m 103 m

7. True or False 1. 1 kg = 1 _________ 103g 2. 102 cm= 1 _________ 1m 3. 103 mm = 1 _________ 1 cm

8. 4. 109 ns = 1_________ 1 ks 5. 1 g = 1 _________ 106 mg 6. 1 kL=1 _________ 103 L

9. Notice a couple of things about the True equalities. • 1) While the metric prefixes were different, the base unit in the ratio was the same. In other words, we were not comparing grams to meters or seconds to volume. There can be ratios comparing these in other types of problems, but it is not something done within a metric conversion ratio. • 2) It did not matter whether the 10x was on the top or bottom of the fraction (numerator or denominator) as long as the other half makes the equality true and equal to 1.

10. We will use these simple equalities as part of a problem-solving technique known as dimensional analysis (DA). • DA is used extensively in chemistry. It is introduced here as a part of metric conversions so that we can learn to use it correctly for the rest of the year. You will not need a calculator. The first is an example done for you.

11. Example: Convert 633 cm to m. Known: 633 cm Unknown: m Conversion Factors: 102 cm = 1 m Solution: 633 cm x 1m = 633 m = 6.33 m 102 cm 102

12. 1. Convert 57 mg to g. Known: Unknown: Conversion Factor (CF): Solution: 2. Convert 7.95 x 106 s to ns Known: Unknown: Conversion Factor (CF): Solution: 3. Convert 1.054 x 104 L to mL Known: Unknown: CF: Solution:

13. Example: Convert 571.2 ng to kg Known: 571.2 ng Unknown: kg Conversions: 1 kg = 103 g 1 g = 109 ng Solution: 571.2 ng x 1 g x 1 kg = 571.2 kg = 109 ng 103g 1012 571.2 x 10-12 kg = 5.712 x 10-10 kg

14. 4. Convert 5.00 km to mm Known: Unknown: Conversions: Solution: 5. 1.7 x 102 mm to cm Known: Unknown: Conversions: Solution: 6. Convert 29 mL to mL Known: Unknown: Conversions: Solution: