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Published byNeal Long Modified over 9 years ago
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- Convert a given result from one system of units to another
DIMENSIONAL ANALYSIS - Convert a given result from one system of units to another - Unit factor method
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Ex 1) A pin measuring 2.85 cm in length. What is its length in inches?
Need an equivalence statement 2.54cm = 1in Divide both sides by 2.54cm Unit Factor 1= 1𝑖𝑛 2.54𝑐𝑚 Multiply any expression by this unit factor and it will not change its value
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Ex 1) A pin measuring 2.85 cm in length. What is its length in inches?
Pin is 2.85cm need to multiply by the unit factor 2.85𝑐𝑚 𝑥 1𝑖𝑛 2.54𝑐𝑚 = 2.85𝑖𝑛 2.54 =1.12𝑖𝑛
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Ex 2) A pencil is 7.00 in long. What is the length in cm?
Convert in cm Need equivalence statement 2.54cm = 1in Unit Factor 2.54𝑐𝑚 1𝑖𝑛 7.00𝑖𝑛 𝑥 2.54𝑐𝑚 1𝑖𝑛 =7𝑥2.54𝑐𝑚=17.8𝑐𝑚
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DIMENSIONAL ANALYSIS 2.54𝑐𝑚 1𝑖𝑛 and 1𝑖𝑛 2.54𝑐𝑚
Unit factors can be derived from each equivalence statement 2.54cm = 1in 2 unit factors 2.54𝑐𝑚 1𝑖𝑛 and 𝑖𝑛 2.54𝑐𝑚
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DIMENSIONAL ANALYSIS 2.54𝑐𝑚 1𝑖𝑛 and 1𝑖𝑛 2.54𝑐𝑚
How to choose – look at direction of required change in cm (need to cancel in – goes in denominator) 2.54𝑐𝑚 1𝑖𝑛 cm in (need to cancel cm – goes in denominator) 1𝑖𝑛 2.54𝑐𝑚
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Ex 3) You want to order a bicycle with a 25
Ex 3) You want to order a bicycle with a 25.5in frame, but the sizes in the catalog are given only in cm. What size should you order? 25.5𝑖𝑛 𝑥 2.54𝑐𝑚 1𝑖𝑛 =7𝑥2.54𝑐𝑚=64.8𝑐𝑚
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Ex 3) A student entered a 10.0-km run. How long is the run in miles?
km mi Equivalence statement 1m = 1.094yd Strategy first km m yards mi Equivalence statements: 1km = 1000m 1m = yd 1760yd = 1 mi
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Ex 3) A student entered a 10.0-km run. How long is the run in miles?
km m 10.0𝑘𝑚 𝑥 1000𝑚 1𝑘𝑚 =1.00𝑥 10 4 𝑚
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Ex 3) A student entered a 10.0-km run. How long is the run in miles?
m yd 1.00𝑥 10 4 𝑚 𝑥 𝑦𝑑 1𝑚 =1.094𝑥 10 4 yd
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Ex 3) A student entered a 10.0-km run. How long is the run in miles?
yd mi Original 10.0 which has 3 sig figs so you want 3 sig figs in your answer 1.094𝑥 10 4 yd 𝑥 1 𝑚𝑖 1760𝑦𝑑 =6.216𝑚𝑖=6.22𝑚𝑖
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Ex 3) A student entered a 10.0-km run. How long is the run in miles?
Can combine all conversions into one step 10.0km 𝑥 1000𝑚 1𝑘𝑚 𝑥 𝑦𝑑 1𝑚 𝑥 1𝑚𝑖 1760𝑦𝑑 =6.22 𝑚𝑖
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DO NOW Ex 4) If a woman has a mass 115lb, what is her mass in grams?
lb g Equivalence Statement 1lb = 453.6g 115𝑙𝑏 𝑥 𝑔 1𝑙𝑏 =5.22𝑥 10 4 𝑔 Ex 5) If a woman has a mass 115lb, what is her mass in grams? dollar cents Equivalence Statement 1 dollar = 100 cents 2.5 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑥 100 𝑐𝑒𝑛𝑡 1 𝑑𝑜𝑙𝑙𝑎𝑟 =250 𝑐𝑒𝑛𝑡𝑠
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Ex 6) Determine the length of a 500.0 mi automobile race in km
mi yd m km Equivalence statements – 1mi = 1760yd 1m = 1.094yd 1km = 1000m 500.0𝑚𝑖 𝑥 1760𝑦𝑑 1𝑚𝑖 𝑥 1𝑚 1.094𝑦𝑑 𝑥 1𝑘𝑚 1000𝑚 =804.7𝑘𝑚
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Ex 7) The average speed of a nitrogen molecule in air at 25C is 515m/s. Convert this speed to miles per hour m/s km/s mi/s mi/min mi/hr Equivalence statements – 1km = 103 1mi = km 60s = 1min 60min = 1hr 15 𝑚 𝑠 𝑥 1𝑘𝑚 𝑚 𝑥 1𝑚𝑖 𝑘𝑚 𝑥 60𝑠 1𝑚𝑖𝑛 𝑥 60𝑚𝑖𝑛 1 ℎ𝑟 =1.15𝑥 10 3 𝑚𝑖/ℎ𝑟
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Ex 8) If you are going 50 mi/hr, how many feet/sec are your going?
mi ft ; hr min sec Equivalence statement 5280 ft=1mi 50 𝑚𝑖 ℎ𝑟 𝑥 5280𝑓𝑡 1𝑚𝑖 𝑥 1ℎ𝑟 60𝑚𝑖𝑛 𝑥 1𝑚𝑖𝑛 1𝑠𝑒𝑐 =70𝑓𝑡/𝑠𝑒𝑐
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Ex 9) Convert 22.50 gal/min to L/s
gal L ; min sec Equivalence statement 1 gal = L 22.50 𝑔𝑎𝑙 𝑚𝑖𝑛 𝑥 𝐿 1𝑔𝑎𝑙 𝑥 1𝑚𝑖𝑛 60𝑠 = =1.420 𝐿/𝑠
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Ex 10)Bamboo can grow up to 60. 0 cm/day
Ex 10)Bamboo can grow up to 60.0 cm/day. Calculate this growth rate in inches per hour cm in ; day hr Equivalence statement 1 in = 2.54 cm 60 𝑐𝑚 𝑑𝑎𝑦 𝑥 1 𝑖𝑛 2.54 𝑐𝑚 𝑥 1 𝑑𝑎𝑦 24 ℎ𝑟 =0.984 𝑖𝑛/ℎ𝑟
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Ex 11)How much bleach (bl) would you need to make a quart of 5% bleach solution (bls)? – (refer to brightstorm youtube video for this question if you get confused) qt oz ; need 5% bls Equivalence statement 1 qt = 32 oz 5oz bs = 5% Bleach 100 oz bls = 100 % bleach solution 1 𝑞𝑡 𝑏𝑙𝑠 𝑥 32 𝑜𝑧 𝑏𝑙𝑠 1 𝑞𝑡 𝑏𝑙𝑠 𝑥 5 𝑜𝑧 𝑏𝑙 100 𝑜𝑧 𝑏𝑙𝑠 =1.6 𝑜𝑧 𝑏𝑙
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Ex 12) A bumblebee flies with a ground speed of 15. 2 m/s
Ex 12) A bumblebee flies with a ground speed of 15.2 m/s. Calculate its speed in km/hr m km ; s min hr Equivalence statement 15.2 𝑚 𝑠 𝑥 1 𝑘𝑚 1000 𝑚 𝑥 60 𝑠 1 𝑚𝑖𝑛 𝑥 60 𝑚𝑖𝑛 1 ℎ𝑟 =54.7 𝑘𝑚/ℎ𝑟
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Ex 13) Convert 0.510 in/ms to km/hr
in cm m km; ms s min hr Equivalence statement 1 in = 2.54cm .510 𝑖𝑛 𝑚𝑠 𝑥 2.54𝑐𝑚 1𝑖𝑛 𝑥 1𝑥 10 −2 𝑚 1𝑐𝑚 𝑥 1𝑘𝑚 1000𝑚 𝑥 1𝑚𝑠 1𝑥 10 −3 𝑠 𝑥 60𝑠 1𝑚𝑖𝑛 𝑥 60𝑚𝑖𝑛 1ℎ𝑟 =46.6 𝑘𝑚/ℎ𝑟
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