Dimensional Amalysis

Discussion questions 1 dozen 12 items What is the meaning of the word DIMENSION? What would dimensional analysis mean for you? Convert 2 dozens eggs into number of eggs. In order to make a conversion we analyze units of measurement. = 1 dozen 12 items

Dimensional Analysis 𝟏 𝒎 𝟏𝟎𝟎 𝒄𝒎 = 𝟏𝟎𝟎 𝒄𝒎 𝟏 𝒎 =𝟏 1m = 100 cm When two measurements are equivalent, a ratio of the two measurements equals 1. 1m = 100 cm 𝟏 𝒎 𝟏𝟎𝟎 𝒄𝒎 = 𝟏𝟎𝟎 𝒄𝒎 𝟏 𝒎 =𝟏 Conversion factor: is a ratio of two equivalent measurements. helps to convert a measurement into different units of measurement. 1 m 100 cm Conversion Factors

Example: Convert 0.35 m into millimeters. 1. Find equivalent relationship between meter and millimeter. 1 m = 1000 mm Two conversion factors can be derived: 𝟏 𝒎 𝟏𝟎𝟎𝟎 𝒎𝒎 =𝟏 𝒂𝒏𝒅 𝟏𝟎𝟎𝟎 𝒎𝒎 𝟏 𝒎 =𝟏

2. Multiply initial value (0 2. Multiply initial value (0.35 m) by the corresponding conversion factor. Thinking question: Which expression is correct to convert 0.35 m into millimeters? 𝟎.𝟑𝟓 𝒎 𝟏 ∙ 𝟏 𝒎 𝟏𝟎𝟎𝟎 𝒎𝒎 𝒐𝒓 𝟎.𝟑𝟓 𝒎 𝟏 ∙ 𝟏𝟎𝟎𝟎 𝒎𝒎 𝟏 𝒎 Incorrect Correct

Meters (m) cancel and millimeters (mm) are left. You need to choose the conversion factor so that the initial unit of measurement cancels in the calculation and the necessary unit of measurement remains. 𝟎.𝟑𝟓 𝒎 𝟏 ∙ 𝟏𝟎𝟎𝟎 𝒎𝒎 𝟏 𝒎 = 𝟎.𝟑𝟓 ∙ 𝟏𝟎𝟎𝟎 𝒎𝒎 𝟏 =𝟑𝟓𝟎 𝒎𝒎 Meters (m) cancel and millimeters (mm) are left.