Chapter 2“Scientific

Measurement”

Metric System &

Converting Units using Dimensional Analysis

Nature of Measurements

Part 1 – Part 1 – numbernumber Part 2 - Part 2 - UnitUnit

Examples:Examples: 2020 grams grams

6.63 x 106.63 x 102 2 m/secm/sec

Measurement - quantitative observation Measurement - quantitative observation consisting of consisting of 2 parts2 parts::

Metric SystemIn 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 massLiter (L) for volumeMeter (m) for length

Seconds (s) for time

Metric Conversion Chart

(Using meters)

Unit Equivalents

Conversion factorsA “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

Dimensional AnalysisA way to analyze and solve problems, by using units (or dimensions) of the measurement

Dimension = a unit (such as g, L, mL)

Analyze = to solveUsing the units to solve the problems.

If the units of your answer are right, chances are you did the math right!

Converting Between UnitsProblems 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.

Simple ExampleSimple Example

We can multiply by a conversion factor to We can multiply by a conversion factor to change the units .change the units .

Problem: 13 inches is how many yards?Problem: 13 inches is how many yards? Known: 36 inches = 1 yard.Known: 36 inches = 1 yard. Write as ratioWrite as ratio 1 yard1 yard

36 inches36 inches 13 inches x 1 yard =13 inches x 1 yard = 0.36 yards0.36 yards

36 inches36 inches

Dimensional AnalysisWrite the given number and unit and draw a “T” chartSet 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.

ExampleConvert 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 bottomThe above problem is just like this

55mm x 10-3m 1mm

Example 2 step conversion

Convert 7000 mL to hectoliters

7000 mL 10-3 L 1 hL__ = 0.07 hL

1 mL 100 L