Unit Conversions

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

• 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

Unit Conversion• Conversion factor

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

57  ·  

73 =53

• 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

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

 = 36  in . + 734  in. 

3  ft − 7 34  in .     = 3 ft   ·(12  in .1  ft )  + 7 34   in. 

More Unit ConversionsFeet and Inches

Tape measures and yard sticks often measure in feet and inches.

• Convert 3 ft - 7 in. to inches:

=  43 34  in .  

= 3  ft  + (7+ 34 ) in .(1  ft12  in . )

More Unit ConversionsFeet and Inches

• Convert 3 ft – 7 in. to feet:

3  ft  − 734in.    = 3  ft  + 7

34  in .(1  ft12  in . )

= 3.65 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  ft12  in . )

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?

55 migal .  (0.264  gal L ).  (1 km0.621   mi )

Dimensional Analysis

1 L  = 0.264 gal

1 km  = 0.621 mi

¿23 .4   kmL

55 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

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