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- Convert a given result from one system of units to another

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1 - 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

2 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 2.54π‘π‘š Multiply any expression by this unit factor and it will not change its value

3 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 2.85π‘π‘š π‘₯ 1𝑖𝑛 2.54π‘π‘š = 2.85𝑖𝑛 2.54 =1.12𝑖𝑛

4 Ex 2) A pencil is 7.00 in long. What is the length in cm?
Convert in οƒ  cm Need equivalence statement 2.54cm = 1in Unit Factor 2.54π‘π‘š 1𝑖𝑛 7.00𝑖𝑛 π‘₯ 2.54π‘π‘š 1𝑖𝑛 =7π‘₯2.54π‘π‘š=17.8π‘π‘š

5 DIMENSIONAL ANALYSIS 2.54π‘π‘š 1𝑖𝑛 and 1𝑖𝑛 2.54π‘π‘š
Unit factors can be derived from each equivalence statement 2.54cm = 1in 2 unit factors 2.54π‘π‘š 1𝑖𝑛 and 𝑖𝑛 2.54π‘π‘š

6 DIMENSIONAL ANALYSIS 2.54π‘π‘š 1𝑖𝑛 and 1𝑖𝑛 2.54π‘π‘š
How to choose – look at direction of required change in οƒ  cm (need to cancel in – goes in denominator) 2.54π‘π‘š 1𝑖𝑛 cm οƒ  in (need to cancel cm – goes in denominator) 1𝑖𝑛 2.54π‘π‘š

7 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 π‘₯ 2.54π‘π‘š 1𝑖𝑛 =7π‘₯2.54π‘π‘š=64.8π‘π‘š

8 Ex 3) A student entered a 10.0-km run. How long is the run in miles?
km οƒ  mi Equivalence statement 1m = 1.094yd Strategy first km οƒ  m οƒ  yards οƒ  mi Equivalence statements: 1km = 1000m 1m = yd 1760yd = 1 mi

9 Ex 3) A student entered a 10.0-km run. How long is the run in miles?
km οƒ  m 10.0π‘˜π‘š π‘₯ 1000π‘š 1π‘˜π‘š =1.00π‘₯ 10 4 π‘š

10 Ex 3) A student entered a 10.0-km run. How long is the run in miles?
m οƒ  yd 1.00π‘₯ 10 4 π‘š π‘₯ 𝑦𝑑 1π‘š =1.094π‘₯ 10 4 yd

11 Ex 3) A student entered a 10.0-km run. How long is the run in miles?
yd οƒ  mi Original 10.0 which has 3 sig figs so you want 3 sig figs in your answer 1.094π‘₯ 10 4 yd π‘₯ 1 π‘šπ‘– 1760𝑦𝑑 =6.216π‘šπ‘–=6.22π‘šπ‘–

12 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 π‘₯ 1000π‘š 1π‘˜π‘š π‘₯ 𝑦𝑑 1π‘š π‘₯ 1π‘šπ‘– 1760𝑦𝑑 =6.22 π‘šπ‘–

13 DO NOW Ex 4) If a woman has a mass 115lb, what is her mass in grams?
lb οƒ  g Equivalence Statement 1lb = 453.6g 115𝑙𝑏 π‘₯ 𝑔 1𝑙𝑏 =5.22π‘₯ 10 4 𝑔 Ex 5) If a woman has a mass 115lb, what is her mass in grams? dollar οƒ  cents Equivalence Statement 1 dollar = 100 cents 2.5 π‘‘π‘œπ‘™π‘™π‘Žπ‘Ÿπ‘  π‘₯ 100 𝑐𝑒𝑛𝑑 1 π‘‘π‘œπ‘™π‘™π‘Žπ‘Ÿ =250 𝑐𝑒𝑛𝑑𝑠

14 Ex 6) Determine the length of a 500.0 mi automobile race in km
mi οƒ  yd οƒ  m οƒ  km Equivalence statements – 1mi = 1760yd 1m = 1.094yd 1km = 1000m 500.0π‘šπ‘– π‘₯ 1760𝑦𝑑 1π‘šπ‘– π‘₯ 1π‘š 1.094𝑦𝑑 π‘₯ 1π‘˜π‘š 1000π‘š =804.7π‘˜π‘š

15 Ex 7) The average speed of a nitrogen molecule in air at 25ο‚°C is 515m/s. Convert this speed to miles per hour m/s οƒ  km/s οƒ  mi/s οƒ  mi/min οƒ  mi/hr Equivalence statements – 1km = 103 1mi = km 60s = 1min 60min = 1hr 15 π‘š 𝑠 π‘₯ 1π‘˜π‘š π‘š π‘₯ 1π‘šπ‘– π‘˜π‘š π‘₯ 60𝑠 1π‘šπ‘–π‘› π‘₯ 60π‘šπ‘–π‘› 1 β„Žπ‘Ÿ =1.15π‘₯ 10 3 π‘šπ‘–/β„Žπ‘Ÿ

16 Ex 8) If you are going 50 mi/hr, how many feet/sec are your going?
mi οƒ  ft ; hr οƒ  min οƒ  sec Equivalence statement 5280 ft=1mi 50 π‘šπ‘– β„Žπ‘Ÿ π‘₯ 5280𝑓𝑑 1π‘šπ‘– π‘₯ 1β„Žπ‘Ÿ 60π‘šπ‘–π‘› π‘₯ 1π‘šπ‘–π‘› 1𝑠𝑒𝑐 =70𝑓𝑑/𝑠𝑒𝑐

17 Ex 9) Convert 22.50 gal/min to L/s
gal οƒ  L ; min οƒ  sec Equivalence statement 1 gal = L 22.50 π‘”π‘Žπ‘™ π‘šπ‘–π‘› π‘₯ 𝐿 1π‘”π‘Žπ‘™ π‘₯ 1π‘šπ‘–π‘› 60𝑠 = =1.420 𝐿/𝑠

18 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 οƒ  in ; day οƒ  hr Equivalence statement 1 in = 2.54 cm 60 π‘π‘š π‘‘π‘Žπ‘¦ π‘₯ 1 𝑖𝑛 2.54 π‘π‘š π‘₯ 1 π‘‘π‘Žπ‘¦ 24 β„Žπ‘Ÿ =0.984 𝑖𝑛/β„Žπ‘Ÿ

19 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 οƒ  oz ; need 5% bls Equivalence statement 1 qt = 32 oz 5oz bs = 5% Bleach 100 oz bls = 100 % bleach solution 1 π‘žπ‘‘ 𝑏𝑙𝑠 π‘₯ 32 π‘œπ‘§ 𝑏𝑙𝑠 1 π‘žπ‘‘ 𝑏𝑙𝑠 π‘₯ 5 π‘œπ‘§ 𝑏𝑙 100 π‘œπ‘§ 𝑏𝑙𝑠 =1.6 π‘œπ‘§ 𝑏𝑙

20 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 οƒ  km ; s οƒ  min οƒ  hr Equivalence statement 15.2 π‘š 𝑠 π‘₯ 1 π‘˜π‘š 1000 π‘š π‘₯ 60 𝑠 1 π‘šπ‘–π‘› π‘₯ 60 π‘šπ‘–π‘› 1 β„Žπ‘Ÿ =54.7 π‘˜π‘š/β„Žπ‘Ÿ

21 Ex 13) Convert 0.510 in/ms to km/hr
in οƒ  cm οƒ  m οƒ  km; ms οƒ  s οƒ  min οƒ  hr Equivalence statement 1 in = 2.54cm .510 𝑖𝑛 π‘šπ‘  π‘₯ 2.54π‘π‘š 1𝑖𝑛 π‘₯ 1π‘₯ 10 βˆ’2 π‘š 1π‘π‘š π‘₯ 1π‘˜π‘š 1000π‘š π‘₯ 1π‘šπ‘  1π‘₯ 10 βˆ’3 𝑠 π‘₯ 60𝑠 1π‘šπ‘–π‘› π‘₯ 60π‘šπ‘–π‘› 1β„Žπ‘Ÿ =46.6 π‘˜π‘š/β„Žπ‘Ÿ


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