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Dimensional Analysis Dimensional Analysis Dimensional analysis: a method of solving problems that involves using equivalence statements and conversion factors; the units (dimensions) guide you through the problem Dimensional Analysis Equivalence statement: an accepted relationship between two units Example: 12 inches = I foot Dimensional Analysis Conversion factors: two possible ratios from an equivalence statement Equivalence statement: 12 inches = I foot Conversion factors: 12 inches I foot and I foot 12 inches Dimensional Analysis Look at the equivalence statements on page 163. Write down the the two possible conversion factors for each equivalence statement. How to use dimensional analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer. Dimensional Analysis Example problems using the equivalence statements on page 163. Be sure to copy the work done on the board. Example #1: 62 cm = ____ in Example #2: _____ yd = 2.45 m Dimensional Analysis You will need to match the metric prefixes you memorized to units and construct your own equivalence statements. Example: kilo is 103 Which is true for the prefix kilo matched to the unit meter (m)? 1 m = 103 km or 103 m = 1 km Dimensional Analysis Which is true for the prefix kilo? 1 m = 103 km or 103 m = 1 km Remember: the “1” always goes with the prefix; the “meaning” you memorized always goes with the unit (without the prefix). Which one above is correct? Dimensional Analysis Write an equivalence statement by matching the unit g (gram) to these prefixes: M, d, c, µ. Dimensional Analysis Use dimensional analysis to solve these problems. Be sure to show all work. a. 3.45 cm = ___ m b. 2.4 X 10-3 g = ___ng c. 6.8 X 105 ms = ___ s Dimensional Analysis Use the equivalence statements on page 163 to do problems 39 and 40 on page 166. One equivalence statement needed that is not listed on page 163: 16 oz = 1 lb