Chapter 2 “ Scientific Measurement ”

1. Chapter 2“Scientific Measurement” Metric System & Converting Units using Dimensional Analysis

2. Nature of Measurements Measurement - quantitative observation consisting of 2 parts: • Part 1 – number • Part 2 - Unit • Examples: • 20 grams • 6.63 x 102 m/sec

3. Metric System • In Science we use the Metric System. • Metric Prefixes are based on powers of 10. • Metric Prefixes can be used with any basic unit of measure. • Gram (g) for mass • Liter (L) for volume • Meter (m) for length • Seconds (s) for time

4. Metric Conversion Chart Unit Equivalents (Using meters)

5. Conversion factors • A “ratio” of equivalent measurements • Start with two things that are the same: one kilometer equals 1000 meters • Write it as an equation (unit equivalent!) 1 km = 1000 m You can also write it as a ratio 1 km or 1000m 1000m 1 km

6. Dimensional Analysis • A way to analyze and solve problems, by using units (or dimensions) of the measurement • Dimension = a unit (such as g, L, mL) • Analyze = to solve • Using the units to solve the problems. • If the units of your answer are right, chances are you did the math right!

7. Converting Between Units • Problems in which measurements with one unit are converted to an equivalent measurement with another unit are easily solved using dimensional analysis. • You basically multiply by one or more unit conversion factors. • You arrange them so the units cancel out and leave you with the desired unit.

8. Simple Example • We can multiply by a conversion factor to change the units . • Problem: 13 inches is how many yards? • Known: 36 inches = 1 yard. • Write as ratio 1 yard 36 inches • 13 inches x 1 yard = 0.36 yards 36 inches

9. Dimensional Analysis • Write the given number and unit and draw a “T” chart • Set up a conversion factor (fraction used to convert one unit to another) • Place the given unit as the denominator of the conversion factor. • Place the desired unit as numerator. • Insert numbers from above table that correspond to each unit in the numerator and denominator. • Cancel the units and solve the problem by multiplying across and dividing by numbers in the denominator.

10. Example • Convert 55 mm to meters 55 mm 10-3_m_ = 0.055 m 1 mm • I use “T” charts as an easier way to set up the ratios. • You multiply numbers across the top and divide by the numbers on the bottom • The above problem is just like this 55mm x 10-3m 1mm

11. Example 2 step conversion • Convert 7000 mL to hectoliters • 7000 mL 10-3 L 1 hL__ = 0.07 hL • 1 mL 100 L