Download - Unit Conversions
![Page 1: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/1.jpg)
Unit Conversions
Washington Technology MagnetIED
![Page 2: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/2.jpg)
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
![Page 3: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/3.jpg)
• 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
![Page 4: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/4.jpg)
Unit Conversion• Conversion factor
– Using a conversion factor to cancel unwanted units is similar to multiplying fractions.
![Page 5: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/5.jpg)
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
![Page 6: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/6.jpg)
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 1Equivalency
![Page 7: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/7.jpg)
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
![Page 8: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/8.jpg)
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 1Equivalency
![Page 9: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/9.jpg)
Conversion of Units – SI System
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
![Page 10: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/10.jpg)
Conversion of UnitsNotes 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.
![Page 11: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/11.jpg)
Conversion of Units – U S System
Desired Unit
Given Unit
• miles to feet: 1 mi = 5280 ft. or
Equal to 1
![Page 12: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/12.jpg)
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
![Page 13: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/13.jpg)
More Unit ConversionsFeet and Inches
![Page 14: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/14.jpg)
More Unit ConversionsFeet and Inches
![Page 15: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/15.jpg)
Use equivalency of units to create conversion factors
Given Unit
• inches to centimeters:
Unit ConversionsBetween U S and SI Systems
Desired Unit
Equal to 1
![Page 16: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/16.jpg)
Conversion of Units between Systems
= 88.1 cm
![Page 17: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/17.jpg)
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.
![Page 18: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/18.jpg)
Unit Conversion• Dimensional Analysis
– Sequential application of conversion factors– Units that appear in both numerator and
denominator cancel
![Page 19: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/19.jpg)
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
![Page 20: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/20.jpg)
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
![Page 21: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/21.jpg)
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
![Page 22: Unit Conversions](https://reader036.vdocuments.us/reader036/viewer/2022062323/56816553550346895dd7cd62/html5/thumbnails/22.jpg)
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