Unit Conversions Introduction to Engineering Design 2012 Project Lead The Way, Inc. Unit Conversion Necessary in science and engineering to work across different systems of measurement or to express quantities in different units within a single system Unit Conversion Conversion factor Multiplied by a quantity to convert the quantity to alternate units A ratio (fraction) in which the quantity in the numerator is equivalent to the quantity in the denominator Contains desired units in the numerator and the given units in the denominator The value of the conversion factor is 1 Conversion Factor = 1 Desired Units Given Units Desired Units Given Units = Desired Units 1 Given Units 1 Unit Conversion

Conversion factor Using a conversion factor to cancel unwanted units is similar to multiplying fractions 5 7 5 = 7 3 3 Writing Numbers SI System Larger Smaller Power of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation 101 deca-

da 10-1 deci- d 102 hecto- h 10-2 centi- c 103 kilo- k 10-3 milli- m

106 Mega- M 10-6 micro- 109 Giga- G 10-9 nano- n Examples: Examples: 10 m = 1 decameter 1,000 L = kiloliters 1,000,000 g = Megagram .01 m = centimeter

.001 L =milliliter .000,001 g = microgram Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation 101 deca- da 10-1 deci- d 102 hecto-

h 10-2 centi- c 103 kilo- k 10-3 milli- m 106 Mega- M 10-6 micro- 109

Giga- G 10-9 nano- n Conversion Factor Given unit in denominator, desired unit in numerator Desired Unit Grams to micrograms: 10-6 g = 1 g or Given Unit Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation Power of 10 Prefix

Abbreviation 101 deca- da 10-1 deci- d 102 hecto- h 10-2 centi- c 103 kilo- k

10-3 milli- m 106 Mega- M 10-6 micro- 109 Giga- G 10-9 nano- n Equal to 1 Equivalency

Grams to micrograms: 10-6 g = 1 g or Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation 101 deca- da 10-1 deci- d 102 hecto-

h 10-2 centi- c 103 kilo- k 10-3 milli- m 106 Mega- M 10-6 micro- 109

Giga- G 10-9 nano- n Desired Unit Megameters to meters: 106 m = 1 Mm or Given Unit Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation 101

deca- da 10-1 deci- d 102 hecto- h 10-2 centi- c 103 kilo- k 10-3 milli-

m 106 Mega- M 10-6 micro- 109 Giga- G 10-9 nano- n Equivalency Equal to 1 Megameters to meters: 106 m = 1 Mm or

Conversion of Units SI System Example: Convert 103.2 cm to meters Desired Unit = 1.032 m Given Unit Power of 10 Prefix Abbreviation 103.2 10 m 10-1 deci- d 10.32 10-1 m 10-2 centi- c 10-3

milli- m 10-6 micro- 10-9 nano- n 10-12 pico- p Powers of 10 -2 1.032 100 m 1.032 m Rules of Exponents 100 = 1 1.032 100 m = 1.032 m 10m 10n = 10m+n

105 10-2 = 105 + 2 = 103 6 10 6 (1) 7 = 10 =10 1 10 Conversion of Units SI System Example: Convert 0.005 kilometers to centimeters 5 0.005 10 cm Powers of 10 0.005 105 cm 0.05 104 cm 0.5 103 cm 5.0 102 cm 50. 101 cm 500. 100 cm 500 cm Conversion of Units SI System Example: Convert 519.67 hectoliters to Megaliters 4 519.67 10 ML

Powers of 10 519.67 10-4 ML 51.967 10-3 ML 5.1967 10-2 ML 0.51967 10-1 ML 0.051967 100 ML 0.051967 ML Conversion of Units Notes on precision: Technically, the number of significant digits should remain the same after conversion (when using exact conversion factors). Measurements are often recorded to incorrect precision. Alternately, converted measurements are often rounded to a given number of decimal places in lieu of considering significant digits. Examples: Nearest tenth of a meter or eighth of an inch If the precision of a measurement is critical, CHECK. Conversion of Units U S System Use equivalency of units to create conversion factors Desired Unit

feet to inches: 1 ft = 12 in. or Given Unit 5280 ft miles to feet: 1 mi = 5280 ft. or 1 mi Equal to 1 Conversion of Units U S System Example: Convert 17.2 yards to feet 3 ft 1 yd ( ) = 51.6 ft 1 yd = 3 ft Note: Technically, the number of significant digits should remain the same after conversion. More Unit Conversions Feet and Inches Tape measures and yard sticks often measure in feet and inches. Convert 3 ft - 7 in. to inches: 3 3 ft 7 in. 4

12 in . 3 = 3 ft + 7 in . 1 ft 4 ( = 36 in . + 7 = 3 43 4 in . ) 3 in . 4 More Unit Conversions Feet and Inches Convert 3 ft 7 in. to decimal feet: 3 3 1 ft 3 ft 7 in . = 3 ft + 7 in . 4 4

12 in . 3 1 ft = 3 ft + 7+ in . 4 12 in . ( ( = 3.65 ft ) ( ) ) Unit Conversions Between U S and SI Systems Use equivalency of units to create conversion factors Inches to centimeters: Desired Unit 2.54 cm 1 in . Given Unit Equal to 1 Conversion of Units Between Systems

Example: Convert 34.7 inches to centimeters 2.54 cm . 1 in. ( ) = 88.1 cm Conversion of Units Between Systems Example: Convert 17 kg to lbm 2.205 lb m . 1 kg ( Note: The number of significant digits is ambiguous in the given quantity assume two significant digits. ) = 3737.48lb lb m m Unit Conversion Dimensional Analysis Sequential application of conversion factors

Units that appear in both numerator and denominator cancel Desired Units Given Units Linking Units Desired Units Given Units = Desired Units 1 1 Given Units Linking Units Dimensional Analysis Example: Convert 345.7 inches to yards 1 ft 1 yd . . 12 in. 3 ft ( ) ( ) = 9.602 yd Note: The number of significant digits should remain the same after conversion. However, if the precision of the original measurement is in question, you may choose to round to a reasonable precision.

Dimensional Analysis Example: An American car company has designed a new high fuel efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter? 1 L = 0.264 gal 55 mi 0.264 gal . gal L ( 1 km . 0.621 mi ) ( ) 1 km = 0.621 mi Dimensional Analysis Example: An American car company has designed a new high fuel efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency

in SI units. What is the fuel usage rate in kilometers per liter? 1 L = 0.264 gal 55 mi 0.264 gal . gal L ( 1 km . 0.621 mi ) ( ) 1 km = 0.621 mi 23.4 km L Dimensional Analysis Example: An American car company has designed a new high fuel efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?

1 L = 0.264 gal 55 mi 0.264 gal . gal L ( 1 km . 0.621 mi ) ( ) 1 km = 0.621 mi 23 km/L