Measurements Conversion Factors Dimensional Analysis 1 Conversion Factors

Measurements Conversion Factors & Dimensional Analysis 1

Conversion Factors Fractions in which the numerator and denominator are quantities expressed in an equality between those units Example: 1 in. = 2. 54 cm Factors: 1 in. and 2. 54 cm 1 in. 2

EXAMPLE 1 Write conversion factors that relate each of the following pairs of units: A. Liters and m. L B. Hours and minutes C. Meters and kilometers 3

SOLUTION 1 A. liters and m. L 1 L and 1000 m. L 1 L = 1000 m. L 1 L B. hours and minutes 1 hr = 60 min 1 hr and 60 min 1 hr C. meters and kilometers 1 km = 1000 m 1 km and 1000 m 1 km 4

Initial and Final Units 1. A person has a height of 2. 0 meters. What is that height in inches? Initial unit = m in Final unit = _______ 2. Blood has a density of 0. 05 g/m. L. If a person lost 0. 30 pints of blood at 18°C, how many ounces of blood would that be? Initial = pints ounces Final unit = _______ 5

How many minutes are in 2. 5 hours? Initial unit 2. 5 hr Conversion factor 2. 5 hr x 60 min 1 hr cancel Final unit = 150 min Answer (2 SF) 6

Using Conversions in the Metric System • 1 • • • Prefix giga- meter megakilohectodeca- Symbol G M k h da Value 1 000 000 meters 1 000 1 00 10 1 • • • deci- meters centimillimicronano d c m (mu) n 0. 1 meters 0. 01 0. 000 001 Base Units (meter, liter, gram, second) 7

EXAMPLE 2 A rattlesnake is 2. 44 m long. How long is the snake in cm? 2. 44 m x 1 cm 0. 01 m = 244 cm 8

EXAMPLE 3 How many seconds are in 1. 4 days? Unit plan: days hr 1. 4 days x 24 hr 1 day x min seconds ? ? 9

SOLUTION 3 Unit plan: days hr min seconds 2 SF 1. 4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min = 1. 2 x 105 sec 10

EXAMPLE 4 What is wrong with the following setup? 1. 4 day x 1 day 24 hr x 60 min 1 hr x 60 sec 1 min 11

SOLUTION 4 1. 4 day x 1 day 24 hr x 60 min 1 hr x 60 sec 1 min Units = day 2 sec/hr 2 Not the final unit needed 12