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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 Given Desired Units Given Units = Units Desired Units 1 Unit Conversion Conversion Factor Given Units 1 = 1
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Transcript of 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
Given Units • Desired UnitsGiven Units
= Desired UnitsDesired Units1
Unit Conversion
Conversion Factor
Given Units1
= 1
Power of 10 Prefix Abbreviation
101 deca- da
102 hecto- h
103 kilo- k
106 Mega- M
109 Giga- G
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
Writing Numbers – SI System
Examples:• 10 m = 1 decameter• 1,000 L = kiloliters• 1,000,000 g = Megagram
Examples:• .01 m = centimeter• .001 L =milliliter• .000,001 g = microgram
Larger Smaller
• Conversion Factor• Given unit in denominator, desired unit in numerator
• Grams to micrograms: 10-6 g = 1 µg or
Conversion of Units – SI System• Prefixes indicate the power of 10
Power of 10 Prefix Abbreviation
101 deca- da
102 hecto- h
103 kilo- k
106 Mega- M
109 Giga- G
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
Desired Unit
Given Unit
• Grams to micrograms: 10-6 g = 1 µg or
Conversion of Units – SI System• Prefixes indicate the power of 10
Power of 10 Prefix Abbreviation
101 deca- da
102 hecto- h
103 kilo- k
106 Mega- M
109 Giga- G
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
Equal to 1
Equivalency
Conversion of Units – SI System• Prefixes indicate the power of 10
Power of 10 Prefix Abbreviation
101 deca- da
102 hecto- h
103 kilo- k
106 Mega- M
109 Giga- G
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
• Megameters to meters: 106 m = 1 Mm or
Desired Unit
Given Unit
Conversion of Units – SI System• Prefixes indicate the power of 10
Power of 10 Prefix Abbreviation
101 deca- da
102 hecto- h
103 kilo- k
106 Mega- M
109 Giga- G
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
• Megameters to meters: 106 m = 1 Mm or
Equal to 1Equivalency
Conversion of Units – SI System
Example: Convert 103.2 cm to meters
=
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
Desired Unit
Given Unit
1.032 m
1.032 m
1.032 ∙ 100 m
10.32 ∙ 10-1 m
103.2 ∙ 10-2 m
Powers of 10
Rules of Exponents
• 100 = 1
• 10m ∙ 10n = 10m+n
105 ∙ 10-2 = 105 + −2 = 103
1.032 ∙ 100 m = 1.032 m
106
10−1 = 106 − (−1)=107
Conversion of Units – SI SystemExample: Convert 0.005 kilometers to centimeters
500 cm
0.5 ∙ 103 cm0.05 ∙ 104 cm0.005 ∙ 105 cm
Powers of 10
5.0 ∙ 102 cm
500. ∙ 100 cm
0.005 ∙105 cm
50. ∙ 101 cm
Conversion of Units – SI SystemExample: Convert 519.67 hectoliters to Megaliters
0.051967 ML
5.1967 ∙ 10-2 ML
51.967 ∙ 10-3 ML
519.67 ∙ 10-4 ML
Powers of 10
0.51967 ∙ 10-1 ML
0.051967 ∙ 100 ML
519.67 ∙10−4 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.
Use equivalency of units to create conversion factors
• feet to inches: 1 ft = 12 in. or
Conversion of Units – U S System
Desired Unit
Given Unit
• miles to feet: 1 mi = 5280 ft. or5280 ft1 mi
Equal to 1
(3 ft1 yd )
Conversion of Units – U S System
Example: Convert 17.2 yards to feet
·
Note: Technically, the number of significant digits should remain the same after conversion.
1 yd = 3 ft
= 51.6 ft
Use equivalency of units to create conversion factors
Given Unit
• Inches to centimeters:
2.54 cm1 in .
Unit ConversionsBetween U S and SI Systems
Desired Unit
Equal to 1
Conversion of Units Between Systems
Example: Convert 34.7 inches to centimeters
= 88.1 cm. (2.54 cm1 in . )
Example: Convert 17 kg to lbm
. (2.205 lbm
1 kg )
Conversion of Units Between Systems
= 37.48 lbm= 37 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
Given Units • Linking UnitsGiven Units
•Desired UnitsLinking Units
= Desired UnitsGiven Units1
Desired Units1
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.
Example: Convert 345.7 inches to yards
.(1 yd3 ft ) = 9.602 yd. (1 ft
12 in . )
Dimensional Analysis
23 km/L55 migal . (0.264 gal
L )
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 km0.621 mi )
Dimensional Analysis
1 L = 0.264 gal
1 km = 0.621 mi
