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The Metric System

The Metric System. and Metric Conversions. Why Use The Metric System?. It is neutral and universally understood. It uses standards that can be replicated by scientists working in any nation. The decimal nature of the metric system makes conversion between metric units simpler.

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The Metric System

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  1. The Metric System and Metric Conversions

  2. Why Use The Metric System? • It is neutral and universally understood. • It uses standards that can be replicated by scientists working in any nation. • The decimal nature of the metric system makes conversion between metric units simpler. • Prefixes serve as convenient modifiers for metric units.

  3. SI Units * *Not actually an SI unit, but commonly used.

  4. Powers of Ten • 101 = 10 • 102 = 10 x 10 = 100 • 103 = 10 x 10 x 10 = 1000 • 104 = 10 x 10 x 10 x 10 = 10,000 • 105 = 10 x 10 x 10 x 10 x 10 = 100,000 • And so on...

  5. Negative Powers of Ten • 10-1 = 1/10 = 0.1 • 10-2 = 1/10 x 1/10 = 1/100 = 0.01 • 10-3 = 1/10 x 1/10 x 1/10 = 1/1000 = 0.001 • 10-4 = 1/10 x 1/10 x 1/10 x 1/10 = 1/10,000 = 0.0 001 • And so on...

  6. Prefixes • Positive powers of ten: • kilo(k) = x 103 = x 1000 • Mega(M) = x 106 = x 1,000,000 • Giga(G) = x 109 = x 1,000,000,000 • Negative powers of ten: • centi(c) = x 10-2 = x 0.01 • milli(m) = x 10-3 = x 0.001 • micro(μ) = x 10-6 = x 0.000 001 • nano(n) = x 10-9 = x 0.000 000 001

  7. Prefixes • Express 1 km in m. • kilo = x 1000 • 1 kilometer = 1000 meters • Express 1 mm in m. • milli = 0.001 • 1 millimeter = 0.001 meter

  8. Prefixes • 1,000,000 phones = ??? • 1 Megaphone (get it?) • 0.000 001 phones = ??? • 1 microphone • 0.000 001 scopes = ??? • 1 microscope • Metric prefixes are even used in literature: • 2000 mockingbirds = • 2 kilomockingbirds

  9. Understanding the Scale of Metric Units 1000 m = 1 mm = 0.1 cm = 0.001 m Width of a human hair ~100 m 100 m = 0.1 mm = 0.01 cm = 0.000 1 m Typical size of a cloud droplet ~ 10 m 10 m = 0.01 mm = 0.001 cm = 0.000 01 m Diameter of a human RBC ~ 7 m 1000 nm = 1 m = 0.001 mm = 0.000 001 m Shortest wavelength of light visible to humans ~ 400 nm 100 nm = 0.1 m = 0.000 1 mm = 0.000 000 1 m Thickness of a cell membrane ~ 10 nm 10 nm = 0.01 m = 0.000 01 mm = 0.000 000 01 m Diameter of a DNA molecule ~2.5 nm 1 nm = 0.001 m = 0.000 001 mm = 0.000 000 001 m

  10. Understanding the Scale of Metric Units 1000 m = 1 km = 0.001 Mm Height of the world’s highest free-falling waterfall = 979 m 100 m = 0.1 km = 0.000 1 Mm Length of the longest blue whale ever measured = 33 m 1000 cm = 10 m = 0.01 km Average height of a human = 1.7 m 1000 mm = 100 cm = 1 m = 0.001 km 1 foot = 30.48 cm 100 mm = 10 cm = 0.1 m Diameter of a golf ball = 4.267 cm 10 mm = 1 cm = 0.01 m Length of an average red ant ~ 5 mm 1000 m = 1 mm = 0.1 cm = 0.001 m

  11. Metric Conversions • Dimensional Analysis • Can be used for non-metric conversions also. • Will set up the problem for you if you do it correctly. • Multiplies by fractions = 1

  12. Metric Conversions • Convert 0.025 kilograms to grams. • Need conversion factor that compares units. • 1 kg = 1000 g • Write a fraction w/ desired unit on top! 1000 g Top and bottom are equal! 0.025 kg x 1 kg

  13. Metric Conversions • Convert 49.6 milliliters to liters. 0.001 L 49.6 mL x = 0.0496 L 1 mL

  14. Metric Conversions • Convert 39.9 centimeters to meters. 0.01 m 39.9 cm x = 0.399 m 1 cm

  15. Two-Step Conversions • Convert 155.3 microliters to milliliters. 0.000 001 L 1 mL x 155.3 µL x = 0.1553 mL 1 µL 0.001 L

  16. Two-Step Conversions • Convert 0.031 Megagrams to kilograms. 1,000,000 g 1 kg x 0.031 Mg x = 31 kg 1 Mg 1000 g

  17. Two-Step Conversions • Convert 195,000 centimeters to kilometers. 0.01 m 1 km x 195,000 cm x = 1.95 km 1 cm 1000 m

  18. Two-Step Conversions • Convert 0.00228 kiloseconds to milliseconds. 1000 s 1 ms x 0.00228 ks x = 2280 ms 1 ks 0.001 s

  19. Non-Metric Conversions • Convert 9500 seconds into hours. 1 min 1 h x 9500 s x = ~2.6 h 60 s 60 min

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