Unit Conversions. O Keefe - LBHS

Transcription

1 Unit Conversions O Keefe - LBHS

2 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

3 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 Given Units Given Units 1 Desired Units Given Units Desired Units = Desired Units 1

4 Unit Conversion Conversion factor Using a conversion factor to cancel unwanted units is similar to multiplying fractions = 5 3

5 Writing Numbers SI System Larger Power of 10 Prefix Abbreviation Smaller Power of 10 Prefix Abbreviation 10 1 deca- da 10 2 hecto- h 10 3 kilo- k 10 6 Mega- M 10 9 Giga- G Examples: 10 m = 1 decameter 1,000 L = kiloliters 1,000,000 g = Megagram 10-1 deci- d 10-2 centi- c 10-3 milli- m 10-6 micro- µ 10-9 nano- n Examples:.01 m = centimeter.001 L =milliliter.000,001 g = microgram

6 Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation 10 1 deca- da 10 2 hecto- h 10 3 kilo- k 10 6 Mega- M 10 9 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 Conversion Factor Given unit in denominator, desired unit in numerator Desired Unit Grams to micrograms: 10-6 g = 1 µg or Given Unit 1 μg 10 6 g

7 Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation 10 1 deca- da 10 2 hecto- h 10 3 kilo- k 10 6 Mega- M 10 9 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 Grams to micrograms: 10-6 g = 1 µg or 1 μg 10 6 g

8 Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation 10 1 deca- da 10 2 hecto- h 10 3 kilo- k 10 6 Mega- M 10 9 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 Megameters to meters: 10 6 m = 1 Mm or 10 6 m 1 Mm Given Unit

9 Conversion of Units SI System Prefixes indicate the power of 10 Power of 10 Prefix Abbreviation 10 1 deca- da 10 2 hecto- h 10 3 kilo- k 10 6 Mega- M 10 9 Giga- G Equivalency 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 Megameters to meters: 10 6 m = 1 Mm or 106 m 1 Mm

10 Conversion of Units SI System Example: Convert cm to meters cm 10 2 m 1 cm = m Desired Unit Given Unit Powers of m m m m 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 pico- p

11 Rules of Exponents 10 0 = m = m 10 m 10 n = 10 m+n = = m 10 n = 10m n = 106 ( 1) = 10 7

12 Conversion of Units SI System Example: Convert kilometers to centimeters km Powers of cm cm cm 10 3 m 1 km cm cm cm 1 cm 10 2 m = cm 500 cm

13 Conversion of Units SI System Example: Convert hectoliters to Megaliters hl 10 2 L 1 hl 1 ML 10 6 L = ML Powers of ML ML ML ML ML ML

14 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.

15 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

16 Conversion of Units U S System Example: Convert 17.2 yards to feet 17.2 yd 3 ft 1 yd = 51.6 ft 1 yd = 3 ft Note: Technically, the number of significant digits should remain the same after conversion.

17 More Unit Conversions Feet and Inches Tape measures and yard sticks often measure in feet and inches. Convert 3 ft in. to inches: 3 ft in. = 3 ft 12 in. 1 ft in. = 36 in in. = in.

18 More Unit Conversions Feet and Inches Convert 3 ft in. to decimal feet: 3 ft in. = 3 ft in. 1 ft 12 in. = 3 ft in. 1 ft 12 in. = 3 ft ft = 3.65 ft

19 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

20 Conversion of Units Between Systems Example: Convert 34.7 inches to centimeters 2.54 cm 34.7 in.. = 88.1 cm 1 in.

21 Conversion of Units Between Systems Example: Convert 17 kg to lb m 17 kg lbm 1 kg = lb m lb m Note: The number of significant digits is ambiguous in the given quantity assume two significant digits.

22 Unit Conversion Dimensional Analysis Sequential application of conversion factors Units that appear in both numerator and denominator cancel Given Units Given Units 1 Linking Units Given Units Desired Units Linking Units Desired Units = Desired Units 1

23 Dimensional Analysis Example: Convert inches to yards 1 ft in in. 1 yd 3 ft = 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.

24 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 = gal 55 mi gal gal L. 1 km mi =? km L 1 km = mi

25 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 = gal 55 mi gal gal L. 1 km mi = 23.4 km L 1 km = mi

26 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 = gal 55 mi gal gal L. 1 km mi = 23 km/l 1 km = mi