The Metric System

1. The Metric System • A decimal system of units for measurements of length, mass, time, etc. • System International (SI) units – a superset of seven units from which all others can be derived.

2. SI Units

3. Common Prefixes

4. Conversion Factor • A relationship between two quantities. • Important – both quantities should include units. • Can be: • metric-to-metric. • English-to-English. • English-to-metric.

5. Conversion Factor • 1 foot = 12 inches • 100 cm = 1 m • 1 inch = 2.54 cm

6. Dimensional Analysis • Uses units with the numerical values. • All units should cancel except those that are desired for the answer. • My method is sometimes referred to as the “fence-post” method. • Remember – answers should be rounded to the proper number of significant figures!

7. Dimensional Analysis • Ex) 45 inches = ? centimeters

8. Dimensional Analysis • 0.054 meters = ? centimeters • Why are these set-ups wrong?

9. Dimensional Analysis • Multi-step problems can be done either all at once or one step at a time. • Ex) 2.50 feet = ? cm

10. Problem-Solving • Read the problem carefully and highlight any numbers and their units. Determine what is known and what is to be solved for. • Plan out your course of action. What conversion factors are needed? Write them down.

11. Problem-Solving • Set-up and organize the problem in a neat and logical fashion making sure units cancel for each step. • Calculate your answer following proper mathematics and round to the proper number of significant digits. • Check your answer and work.

12. Dimensional Analysis • Ex) 15 pints = ? L

13. Dimensional Analysis • 55 miles per hour = ? meters per second • How long will it take to travel 5.0 km at this speed?

14. Measuring Mass and Volume • Matter = anything that occupies space and has mass. • The SI unit of mass is the kilogram. • Volume is a derived unit and is the amount of space occupied by matter. • Based on the SI system, the standard unit would be a meter x meter x meter or cubic meter (m3).

15. Measuring Mass and Volume • However, this is too large to use in practical uses. • 1 milliliter (mL) is defined as a cube that measures 1 cm x 1 cm x 1 cm. • Thus, 1 mL = 1 cm3 or 1 cc.

16. Volume Conversions • A block measures 12 inches by 6.5 inches by 2.5 inches. What is the volume of this block in Liters?

17. Temperature • Temperature is the measurement of the amount of heat a substance has. • Heat flows from warmer to colder objects. • SI unit is the Kelvin. • Metric unit is Celsius. • English unit is Fahrenheit.

19. Temperature Conversions • oF = (1.8 x oC) + 32 • oC = (oF – 32) / 1.8 • K = oC + 273.15

20. Temperature Conversions • Convert 72oC to Fahrenheit • Convert 65oF to Celsius • Convert 225K to Fahrenheit

21. Density • Density is the ratio of the mass of the substance to its volume. • A substance can sometimes be identified by its density. • Standard units for solids and liquids are grams per milliliter.

22. Density • Can use the density of a substance as a conversion factor. • Density of Aluminum = 2.70 g/mL. • Thus, every 1 mL of Al = 2.70 g. • What volume would a mass of a 452 gram block of Al occupy?

23. Density • A 2.50 gallon container of a liquid has a mass of 16.7 pounds. What is the density of the liquid in grams per milliliter?

24. Density • The density of gold is 19.3 g/mL. What is the mass in grams of a gold bar measuring 6.0 in. x 4.0 in. x 2.0 in.?