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Dimensional Analysis or the Factor Label Method

This guide explores Dimensional Analysis, focusing on the Factor-Label Method for solving step problems involving unit conversions. Key base units are defined: time (second), length (meter), mass (gram), and volume (liter). The metric system is examined through prefixes like kilo-, mega-, and milli-, each with unique symbols indicating multiples or fractions of base units. Practical examples illustrate converting kilograms to grams and nanoliters to liters, enhancing comprehension of unit relationships and dimensional analysis techniques.

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Dimensional Analysis or the Factor Label Method

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  1. Dimensional Analysis or the Factor Label Method 1 Step Problems

  2. Base Units Base Unit – a unit of measurement that does not have a prefix Time – second (s) Length – meter (m) Mass – gram (g) Volume – liter (L)

  3. Metric Prefixes • Prefix – precedes a base unit of measure to indicate a multiple or a fraction of the unit • Each prefix has a unique symbol that is added to the beginning of the base unit • Example: the prefix kilo- has a symbol of k- the base unit meter has a symbol of m add the prefix to the base unit: kilometer, km

  4. Larger than the base unit Mega- (M) 1 x 106 g = 1 Mg means 1,000,000 Kilo- (k) 1 x 103 L = 1 kL means 1,000 Hecto- (h) 1 x 102 m = 1 hm means 100 Deca- (da) 1 x 101 g = 1 dag means 10

  5. Smaller than the base unit deci- (d) 1 g = 1 x 101 dg means 1/10 centi- (c) 1 L = 1 x 102cL means 1/100 milli- (m) 1 m = 1 x 103 mm means 1/1,000

  6. Smaller than the base unit micro- () 1 g = 1 x 106g means 1/1,000,000 nano- (n) 1 L = 1 x 109nL means 1/1,000,000,000 Angstrom (Å) 1 m = 1 x 1010Å means 1/10,000,000,000 pico- (p) 1 g = 1 x 1012pg means 1/1,000,000,000,000

  7. Dimensional Analysis or the Factor Label Method 1 step problem Example – How many grams are in 3.42 kg? • Write down your known 3.42 kg

  8. 1 Step Problem Example – How many grams are in 3.42 kg? • Write down the conversion that involves your known unit on bottom and the unit you want to go to on top. 3.42 kg 1000 g 1 kg

  9. 1 Step Problem You can either write the conversion in a “ladder” 3.42 kg 1000 g 1 kg Or as a multiplication factor: 3.42 kg x 1000 g 1 kg

  10. 1 Step Problem 3. Cancel out units and solve. • Remember if you have the same unit on top and on bottom, they cancel out. 3.42 kg x 1000 g =3420 g 1 kg

  11. Practice How many Liters are in 1.5 x 106nL? = 1.5 x 10-3 L

  12. Practice How many milligrams are in 260 grams? = 260,000 mg

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