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Understanding Scientific Measurement: The Metric System and Dimensional Analysis

This chapter explores the essentials of scientific measurement, emphasizing the Metric System and the process of converting units through dimensional analysis. Measurement consists of two key parts: a number and a unit, illustrated by examples like 20 grams and 6.63 x 10^2 m/sec. The Metric System's use of prefixes based on powers of ten enables clear communication in scientific contexts. Dimensional analysis techniques are discussed to simplify unit conversions, allowing for accurate problem-solving in real-world applications, like converting inches to yards or milliliters to hectoliters.

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Understanding Scientific Measurement: The Metric System and Dimensional Analysis

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  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

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