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Dimensional Analysis for Conversions: Mastering Measurement Relationships

This comprehensive guide explores dimensional analysis for unit conversions, equipping you to solve real-world problems confidently. Learn to identify known and unknown units, draw dimensional "jumps," and utilize charts for unit relationships. Step-by-step examples, such as converting 9.3 cups to quarts and 6 minutes to seconds, illustrate essential concepts. Discover the importance of consistent units of measurement and compare various metric units using the ladder method. Practice challenges and conversion exercises are included to reinforce your understanding and skills.

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Dimensional Analysis for Conversions: Mastering Measurement Relationships

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  1. Dimensional Analysis for Conversions

  2. Write the KNOWN, identify the UNKNOWN. • EX. How many quarts is 9.3 cups? 9.3 cups = ? quarts

  3. Write the KNOWN, identify the UNKNOWN. • EX. How many quarts is 9.3 cups? 9.3 cups = ? quarts

  4. Draw the dimensional “jumps”. 9.3 cups = ? quarts 9.3 cups x * Use charts or tables to find relationships

  5. Insert relationship so units cancel. quart 1 9.3 cups x 4 cups *units of known in denominator (bottom) first *** units of unknowns in numerator (top

  6. Cancel units 1 quart 9.3 cups x 4 cups

  7. Do Math 1 quart 9.3 cups x 4 cups • Follow order of operations! • Multiply values in numerator • If necessary multiply values in denominator • Divide.

  8. Do the Math 1 quart 9.3 x 1 9.3 cups x = 4 cups 1 x 4 9.3 = 2.325 quarts = 4

  9. Try this: • How many seconds are in 6 minutes? ____ seconds (6o seconds = 1 minute) • How many centimeters are in 27 inches? ____ centimeters (1 inch = 2.54 centimeters)

  10. Metric Conversions Ladder Method T. Trimpe 2008 http://sciencespot.net/

  11. Why do we need units of measurement? • If I tell you that I weight 200, it will make a difference whether it is pounds or kilograms. • Kilograms are 2.2 times heavier than a pound!

  12. Systems of Measurement • The English system was based on the King’s measurement. • Inch was based on the width of his thumb • Feet were the length of one foot • Yards were the circumference of the king’s waist But what happens when the king dies and his son’s measurements are LARGER?

  13. International System of Units (SI units) • Metrics are used by SCIENTISTS • Based on standardized measurements • Used worldwide. • Based on multiples.

  14. Ladder Method 1 2 3 KILO1000Units HECTO100Units DEKA10Units DECI0.1Unit CENTI0.01Unit MILLI0.001Unit MetersLitersGrams

  15. Conversion Practice Compare using <, >, or =. 56 cm 6 m 7 g 698 mg Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm 14 km = _______ m 109 g = _______ kg 250 m = _______ km

  16. Metric Conversion Challenge Write the correct abbreviation for each metric unit. Kilogram _____ Milliliter _____ Kilometer _____ Meter _____ Centimeter _____ Gram _____ Liter _____ Milligram _____ Try these conversions.. 2000 mg = _______ g 5 L = _______ mL 16 cm = _______ mm 104 km = _______ m 198 g = _______ kg 2500 m = _______ km

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