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Unit Conversions

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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

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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 Unit Conversion Conversion Factor = 1

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

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Conversion of Units – SI System Prefixes indicate the power of 10 Power of 10PrefixAbbreviation 10 1 deca-da 10 2 hecto-h 10 3 kilo-k 10 6 Mega-M 10 9 Giga-G Power of 10PrefixAbbreviation 10 -1 deci-d 10 -2 centi-c 10 -3 milli-m 10 -6 micro-µ 10 -9 nano-n Desired Unit Given Unit

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Conversion of Units – SI System Prefixes indicate the power of 10 Power of 10PrefixAbbreviation 10 1 deca-da 10 2 hecto-h 10 3 kilo-k 10 6 Mega-M 10 9 Giga-G Power of 10PrefixAbbreviation 10 -1 deci-d 10 -2 centi-c 10 -3 milli-m 10 -6 micro-µ 10 -9 nano-n Equal to 1 Equivalency

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Conversion of Units – SI System Prefixes indicate the power of 10 Power of 10PrefixAbbreviation 10 1 deca-da 10 2 hecto-h 10 3 kilo-k 10 6 Mega-M 10 9 Giga-G Power of 10PrefixAbbreviation 10 -1 deci-d 10 -2 centi-c 10 -3 milli-m 10 -6 micro-µ 10 -9 nano-n Megameters to meters: 10 6 m = 1 Mm or Desired Unit Given Unit

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Conversion of Units – SI System Prefixes indicate the power of 10 Power of 10PrefixAbbreviation 10 1 deca-da 10 2 hecto-h 10 3 kilo-k 10 6 Mega-M 10 9 Giga-G Power of 10PrefixAbbreviation 10 -1 deci-d 10 -2 centi-c 10 -3 milli-m 10 -6 micro-µ 10 -9 nano-n Equal to 1 Equivalency

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Conversion of Units – SI System Power of 10 PrefixAbbreviation 10 -1 deci-d 10 -2 centi-c 10 -3 milli-m 10 -6 micro-µ 10 -9 nano-n 10 -12 pico-p Desired Unit Given Unit 1.032 m

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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.

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

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Conversion of Units – U S System Note: Technically, the number of significant digits should remain the same after conversion. 1 yd = 3 ft = 51.6 ft

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More Unit Conversions Feet and Inches

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More Unit Conversions Feet and Inches

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

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Conversion of Units between Systems = 88.1 cm

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Conversion of Units between Systems = 37.48 lb m = 37 lb m Note: The number of significant digits is ambiguous in the given quantity – assume two significant digits.

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

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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. = 9.602 yd Dimensional Analysis

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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? Dimensional Analysis

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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? Dimensional Analysis

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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? Dimensional Analysis

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Quiz How many significant figures are there in the number 45.07 cm? (5 points) Express the operations correctly (5 points each) a. 34.56 cm + 3 cm = b.

Quiz How many significant figures are there in the number 45.07 cm? (5 points) Express the operations correctly (5 points each) a. 34.56 cm + 3 cm = b.

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