unit conversions

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

Unit Conversion

Conversion Factor = 1

Unit Conversion• Conversion factor

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

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

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

Equal to 1Equivalency

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

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.

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

Note: Technically, the number of significant digits should remain the same after conversion.

1 yd = 3 ft

= 51.6 ft

More Unit ConversionsFeet and Inches

More Unit ConversionsFeet and Inches

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

Conversion of Units between Systems

= 88.1 cm

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

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

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

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

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