Unit Conversions Notes Unit Conversion Necessary in science

Unit Conversion • Necessary in science and engineering to work across different systems of

Unit Conversion • Conversion factor – Multiplied by a quantity to convert the quantity

Unit Conversion • Conversion factor – Using a conversion factor to cancel unwanted units

Writing Numbers – SI System Larger Note: Conversion Factors are in the back of

Conversion of Units – SI System • Prefixes indicate the power of 10 Prefix

Conversion of Units – SI System Desired Unit 1. 032 m Given Unit Powers

Rules of Exponents • 1. 032 ∙ 100 m = 1. 032 m

Conversion of Units – SI System Powers of 10 105 0. 005 ∙ cm

Conversion of Units – SI System Powers of 10 519. 67 ∙ 10 -4

Conversion of Units Notes on precision: • The number of significant digits should remain

Conversion of Units – U S System Desired Unit Given Unit • miles to

Conversion of Units – U S System = 51. 6 ft 1 yd =

Unit Conversions Between U S and SI Systems Use equivalency of units to create

Conversion of Units Between Systems = 88. 1 cm

Conversion of Units Between Systems = 37 37. 48 lbm Note: The number of

Unit Conversion • Dimensional Analysis – Sequential application of conversion factors – Units that

Dimensional Analysis = 9. 602 yd Note: The number of significant digits should remain

Dimensional Analysis Example: An American car company has designed a new high fuel efficiency

Practice • Complete Activity 3. 2 h Unit Conversion Homework.

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Unit Conversions Notes

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

Unit Conversion • Conversion factor – Using a conversion factor to cancel unwanted units is similar to multiplying fractions

Writing Numbers – SI System Larger Note: Conversion Factors are in the back of your Engineering Notebook. Smaller 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- µ 109 Giga- G 10 -9 nano- n Examples: • 10 m = 1 decameter • 1, 000 L = kiloliters • 1, 000 g = Megagram • . 01 m = centimeter • . 001 L =milliliter • . 000, 001 g = microgram

Conversion of Units – SI System • Prefixes indicate the 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- µ 109 Giga- G 10 -9 nano- n Desired Unit Given Unit

Conversion of Units – SI System Desired Unit 1. 032 m Given Unit Powers of 10 103. 2 ∙ 10 -2 m 10. 32 ∙ 10 -1 m 1. 032 ∙ 100 1. 032 m m Power of 10 Prefix Abbreviation 10 -1 deci- d 10 -2 centi- c 10 -3 milli- m 10 -6 micro- µ 10 -9 nano- n 10 -12 pico- p

Rules of Exponents • 1. 032 ∙ 100 m = 1. 032 m

Conversion of Units – SI System Powers of 10 105 0. 005 ∙ cm 0. 05 ∙ 104 cm 0. 5 ∙ 103 cm 5. 0 ∙ 102 cm 50. ∙ 101 cm 500. ∙ 100 cm Include examples in your in notes. 500 cm

Conversion of Units – SI System 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: • 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 Desired Unit Given Unit • miles to feet: 1 mi = 5280 ft. or Equal to 1

Conversion of Units – U S System = 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

Unit Conversions Between U S and SI Systems Use equivalency of units to create conversion factors • Inches to centimeters: Desired Unit Given Unit Equal to 1

Conversion of Units Between Systems = 88. 1 cm

Conversion of Units Between Systems = 37 37. 48 lbm Note: The number of significant digits is ambiguous in the given quantity – assume two significant digits.

Unit Conversion • Dimensional Analysis – Sequential application of conversion factors – Units that appear in both numerator and denominator cancel

Dimensional Analysis = 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?

Practice • Complete Activity 3. 2 h Unit Conversion Homework.