U3 Unit Conversions - Lancaster High School

[Pages:7]Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

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

Unit 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

Conversion Factor = 1

GGiivveenn UUnniittss 1

?

Desired Units Desired Units Given Units = Desired1Units

Unit Conversion

? Conversion factor

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

57 5 7 ? 3= 3

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

Writing Numbers ? SI System

Larger Power of 10

Prefix

Abbreviation

101

deca-

da

102

hecto-

h

103

kilo-

k

106

Mega-

M

109

Giga-

G

Examples:

? 10 m = 1 decameter ? 1,000 L = kiloliters ? 1,000,000 g = Megagram

Smaller Power of 10

Prefix

Abbreviation

10-1

deci-

d

10-2

centi-

c

10-3

milli-

m

10-6

micro-

?

10-9

nano-

n

Examples:

? .01 m = centimeter ? .001 L =milliliter ? .000,001 g = microgram

Conversion of Units ? SI System

? Prefixes indicate the power of 10

Power of 10

101 102 103 106 109

Prefix

decahectokiloMegaGiga-

Abbreviation

da h k M G

Power of 10

10-1 10-2 10-3 10-6 10-9

Prefix

decicentimillimicronano-

Abbreviation

d c m ? n

? Conversion Factor

? Given unit in denominator, desired unit in numerator

Desired Unit

?

Grams to micrograms:

10-6 g = 1 ?g or

1 g 10-6 g

Given Unit

Conversion of Units ? SI System

? Prefixes indicate the power of 10

Power of 10

101 102 103 106 109

Prefix

decahectokiloMegaGiga-

Abbreviation

da h k M G

Power of 10

10-1 10-2 10-3 10-6 10-9

Prefix

decicentimillimicronano-

Abbreviation

d c m ? n

Equal to 1

Equivalency

?

Grams to micrograms:

10-6 g = 1 ?g or

1 g 10-6 g

Conversion of Units ? SI System

? Prefixes indicate the power of 10

Power of 10

101 102 103 106 109

Prefix

decahectokiloMegaGiga-

Abbreviation

da h k M G

Power of 10

10-1 10-2 10-3 10-6 10-9

Prefix

decicentimillimicronano-

Abbreviation

d c m ? n

Desired Unit

? Megameters to meters: 106 m = 1 Mm or 106 m 1 Mm

Given Unit

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

Conversion of Units ? SI System

? Prefixes indicate the power of 10

Power of 10

101 102 103 106 109

Prefix

decahectokiloMegaGiga-

Abbreviation

da h k M G

Power of 10

10-1 10-2 10-3 10-6 10-9

Prefix

decicentimillimicronano-

Abbreviation

d c m ? n

Equivalency

Equal to 1

?

Megameters to meters:

106 m = 1 Mm

or

106 m 1 Mm

Conversion of Units ? SI System

Example: Convert 103.2 cm to meters

103.2 cm ?

10-2 m 1 cm

=

Desired Unit

1.032 m

Given Unit

Powers of 10

103.2 10-2 m 10.32 10-1 m 1.032 100 m

1.032 m

Power of 10 10-1 10-2 10-3 10-6 10-9 10-12

Prefix

decicentimillimicronanopico-

Abbreviation

d c m ? n p

Rules of Exponents

? 100 = 1 1.032 100 m = 1.032 m

? 10m 10n = 10m+n 105 10-2 = 105 + -2 = 103

?

10m 10n

= 10m-n

106 10-1

=

106

-

(-1)

=

107

Conversion of Units ? SI System

Example: Convert 0.005 kilometers to centimeters

0.005 km ?

103m 1 km

?

1 cm 10-2 m

= 0.005 105 cm

Powers of 10

0.005 105 cm 0.05 104 cm

0.5 103 cm 5.0 102 cm 50. 101 cm 500. 100 cm

500 cm

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

Conversion of Units ? SI System

Example: Convert 519.67 hectoliters to Megaliters

519.67 hL ?

102 L 1 hL

?

1 ML 106 L

=

519.6710-4 ML

Powers of 10

519.67

10-4 ML

51.967 10-3 ML

5.1967 10-2 ML

0.51967 10-1 ML

0.051967 100 ML

0.051967 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.

Conversion of Units ? U S System

Use equivalency of units to create conversion factors

Desired Unit

?

feet to inches:

1 ft = 12 in. or

12 in. 1 ft

Given Unit

? miles to feet: 1 mi = 5280 ft. or 5280 ft 1 mi

Equal to 1

Conversion of Units ? U S System

Example: Convert 17.2 yards to feet

3 ft

17.2 yd ? 1 yd = 51.6 ft

1 yd = 3 ft

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

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

More Unit Conversions Feet and Inches

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

?

Convert

3

ft

-

7

3 4

in.

to

inches:

3

12 in.

3 ft- 7 4 in. = 3 ft ? 1 ft

=

36

in.

+

7

3 4

in.

=

43

3 4

in.

+

7

3 4

in.

More Unit Conversions Feet and Inches

?

Convert

3

ft

?

7

3 4

in.

to

decimal

feet:

3 ft - 734 in.

= 3 ft + 734 in.

1 ft 12 in.

= 3 ft +

7+

3 4

in.

1 ft 12 in.

= 3 ft + 0.65 ft

= 3.65 ft

Unit Conversions Between U S and SI Systems

Use equivalency of units to create conversion factors

? Inches to centimeters:

Desired Unit

2.54 cm 1 in.

Given Unit

Equal to 1

Conversion of Units Between Systems

Example: Convert 34.7 inches to centimeters

2.54 cm

34.7 in. . 1 in. = 88.1 cm

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

Conversion of Units Between Systems

Example: Convert 17 kg to lbm

17 kg .

2.205 lbm 1 kg

= 37.l4b8mlbm

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 Given1 Units

?

Linking Units Given Units

?

Desired Units Linking Units =

Desired Units Desired1Units

Dimensional Analysis

Example: Convert 345.7 inches to yards

1 ft 1 yd

345.7 in. . 12 in. . 3 ft

= 9.602 yd

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.

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?

1 L = 0.264 gal

55 mi 0.264 gal

gal .

L

1 km . 0.621 mi

1 km = 0.621 mi

? km =L

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Unit Conversion

Introduction to Engineering Design ? Lesson 1.3 - Measurement and Statistics

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?

1 L = 0.264 gal

55 mi 0.264 gal

gal .

L

1 km . 0.621 mi

1 km = 0.621 mi

23.4 km =

L

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?

1 L = 0.264 gal

55 mi 0.264 gal

gal .

L

1 km . 0.621 mi

= 23 km/L

1 km = 0.621 mi

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