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Dimensional Analysis

Dimensional Analysis. Jill Luckey Beaufort Academy. Purpose. Dimensional Analysis, also known as “Factor Labeling”, is a systematic method used for the conversion of units, typically from metric to non-metric or vice-versa.

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Dimensional Analysis

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  1. Dimensional Analysis Jill Luckey Beaufort Academy

  2. Purpose • Dimensional Analysis, also known as “Factor Labeling”, is a systematic method used for the conversion of units, typically from metric to non-metric or vice-versa. • ie: if you wanted to know how many inches are in 3.3 km, you would use dimensional analysis • Note: this conversion seems unimportant, but the METHOD is important and will be vital to your existence as a Chemistry or Physics student.

  3. Table of Common Conversions Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm Mass 1 oz = 28 g Memorize These! Time 1 day = 24 hr 1 yr = 365 day 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s Volume 1 ml = 1 cm3 1 gal = 3.8 L 1 m3 = 1000 L Note: You should know all metric to metric conversions!

  4. Mathematical Basis • Let’s take our example, 3.3 km = __?_ in • What happens if we multiply 3.3 km by 1? • What do these represent? • 12/12; 5280/5280; 3.14/3.14 • What do these represent? • 12 in / 1 foot; 5280 ft / 1 mile We are not changing the meaning of the value 3.3 km They all represent the number 1 These all represent the number “1” since the numerator equals the denominator in meaning (not in number or unit)

  5. Conversions as Fractions Now we know we can take our conversions and make fractions out of them ie: 1 km = 0.6 mi can be written as: 1 km 0.6 mi 0.6 mi 1 km or as…

  6. New Conversion Tables - Length 1 km 0.6 mi 0.6 mi 1 km Shown in Pairs 1 mi 5280 ft 5280 ft 1 mi More than just advice: Start thinking of the entire table on slide 3 in this manner. 1 ft 12 in 12 in 1 ft 1 m 39.3 in 39.3 in 1 ft 1 in 2.54 cm 2.54 cm 1 in

  7. Let’s Factor Label to Convert! 3.3 km = __?__ in Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm Let’s copy our length conversions here: STOP when the unit you want is in the numerator! Step 1: Copy the given ? in 3.3 km 0.6 mi 5280 ft 12 in = 1.3 x 10 5 in 1 km 1 mi 1 ft Step 2: Draw a long horizontal line (indicating the divide b/w numerator and denominator) Note: sig figs should equal that found in given! Step 3: Print the unit you’re solving for above the given Step 4: Draw vertical line(s) to separate portions of the conversion Step 5: Write the conversion factor WHICH CANCELS OUT the unit currently in the numerator. Start with the DENOMINATOR, and plan out your conversion strategy (ie: km to mi; mi to ft, ft to in) Step 6: Stop, Drop, and Calculate!

  8. Practice 1 Volume 1 ml = 1 cm3 1 gal = 3.8 L 1 m3 = 1000 L a. 2.9 m3 = __?__ gal Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm b. 9.9 in = __?__ km Time 1 day = 24 hr 1 yr = 365 day 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s c. 8.1 s = __?__ yr

  9. Practice 2 Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm a. 33 mph = __?__ cm/s Time 1 day = 24 hr 1 yr = 365 day 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s b. $2.55/gal = __?__ Eu/L Volume 1 ml = 1 cm3 1 gal = 3.8 L 1 m3 = 1000 L c. 1.5 cm3/s = __?__ gal/day 1 Eu = $1.18 US

  10. Practice 1 (Answers) Volume 1 ml = 1 cm3 1 gal = 3.8 L 1 m3 = 1000 L a. 2.9 m3 = __?__ gal ? gal 1 gal 2.9 m3 1000 L = 760 gal 1 m3 3.8 L Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm b. 9.9 in = __?__ km ? km 9.9 in 1 m 1 km = 2.5 x 10 -4 km 39.3 in 1000 m Time 1 day = 24 hr 1 yr = 365 day 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s c. 8.1 s = __?__ yr ? yr 8.1 s 1 hr 1 day 1 yr = 2.6 x 10-7 yr 3600 s 24 hr 365 day

  11. Practice 2 (Answers) Length 1 km = 0.61 mi 1 mi = 5280 ft 1 ft = 12 in 1 m = 39.3 in 1 in = 2.54 cm a. 33 mph = __?__ cm/s ? cm/s 33 mi 5280 ft 12 in 2.54 cm 1 hr = 1.5 x 103 cm/s 1 hr 1 mi 1 ft 1 in 3600 s Time 1 day = 24 hr 1 yr = 365 day 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s b. $2.55/gal = __?__ Eu/L ? Eu/L 2.55 dol 1 Eu 1 gal = 0.569 Eu/L 1 gal 1.18 dol 3.8 L Volume 1 ml = 1 cm3 1 gal = 3.8 L 1 m3 = 1000 L c. 1.5 cm3/s = __?__ gal/day ? Gal/day 1.5 cm3 1 ml 1 L 1 gal 3600 s 24 hr = 34 gal/day 1 s 1 cm3 1000 ml 3.8 L 1 hr 1 day 1 Eu = $1.18 US

  12. HOMEWORK: • Handout – do all problems on Dimensional Analysis

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