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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= 1ππ 2.54ππ 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 2.85ππ π₯ 1ππ 2.54ππ = 2.85ππ 2.54 =1.12ππ

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**Ex 2) A pencil is 7.00 in long. What is the length in cm?**

Convert in ο cm Need equivalence statement 2.54cm = 1in Unit Factor 2.54ππ 1ππ 7.00ππ π₯ 2.54ππ 1ππ =7π₯2.54ππ=17.8ππ

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**DIMENSIONAL ANALYSIS 2.54ππ 1ππ and 1ππ 2.54ππ**

Unit factors can be derived from each equivalence statement 2.54cm = 1in 2 unit factors 2.54ππ 1ππ and ππ 2.54ππ

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**DIMENSIONAL ANALYSIS 2.54ππ 1ππ and 1ππ 2.54ππ**

How to choose β look at direction of required change in ο cm (need to cancel in β goes in denominator) 2.54ππ 1ππ cm ο in (need to cancel cm β goes in denominator) 1ππ 2.54ππ

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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? 25.5ππ π₯ 2.54ππ 1ππ =7π₯2.54ππ=64.8ππ

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**Ex 3) A student entered a 10.0-km run. How long is the run in miles?**

km ο mi Equivalence statement 1m = 1.094yd Strategy first km ο m ο yards ο 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 ο m 10.0ππ π₯ 1000π 1ππ =1.00π₯ 10 4 π

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**Ex 3) A student entered a 10.0-km run. How long is the run in miles?**

m ο yd 1.00π₯ 10 4 π π₯ π¦π 1π =1.094π₯ 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 ο 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 ππ 1760π¦π =6.216ππ=6.22ππ

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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 π₯ 1000π 1ππ π₯ π¦π 1π π₯ 1ππ 1760π¦π =6.22 ππ

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**DO NOW Ex 4) If a woman has a mass 115lb, what is her mass in grams?**

lb ο g Equivalence Statement 1lb = 453.6g 115ππ π₯ π 1ππ =5.22π₯ 10 4 π Ex 5) If a woman has a mass 115lb, what is her mass in grams? dollar ο cents Equivalence Statement 1 dollar = 100 cents 2.5 πππππππ π₯ 100 ππππ‘ 1 ππππππ =250 ππππ‘π

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**Ex 6) Determine the length of a 500.0 mi automobile race in km**

mi ο yd ο m ο km Equivalence statements β 1mi = 1760yd 1m = 1.094yd 1km = 1000m 500.0ππ π₯ 1760π¦π 1ππ π₯ 1π 1.094π¦π π₯ 1ππ 1000π =804.7ππ

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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 ο km/s ο mi/s ο mi/min ο mi/hr Equivalence statements β 1km = 103 1mi = km 60s = 1min 60min = 1hr 15 π π π₯ 1ππ π π₯ 1ππ ππ π₯ 60π 1πππ π₯ 60πππ 1 βπ =1.15π₯ 10 3 ππ/βπ

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**Ex 8) If you are going 50 mi/hr, how many feet/sec are your going?**

mi ο ft ; hr ο min ο sec Equivalence statement 5280 ft=1mi 50 ππ βπ π₯ 5280ππ‘ 1ππ π₯ 1βπ 60πππ π₯ 1πππ 1π ππ =70ππ‘/π ππ

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**Ex 9) Convert 22.50 gal/min to L/s**

gal ο L ; min ο sec Equivalence statement 1 gal = L 22.50 πππ πππ π₯ πΏ 1πππ π₯ 1πππ 60π = =1.420 πΏ/π

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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 ο in ; day ο hr Equivalence statement 1 in = 2.54 cm 60 ππ πππ¦ π₯ 1 ππ 2.54 ππ π₯ 1 πππ¦ 24 βπ =0.984 ππ/βπ

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Ex 11)How much bleach (bl) would you need to make a quart of 5% bleach solution (bls)? β (refer to brightstorm youtube video for this question if you get confused) qt ο oz ; need 5% bls Equivalence statement 1 qt = 32 oz 5oz bs = 5% Bleach 100 oz bls = 100 % bleach solution 1 ππ‘ πππ π₯ 32 ππ§ πππ 1 ππ‘ πππ π₯ 5 ππ§ ππ 100 ππ§ πππ =1.6 ππ§ ππ

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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 ο km ; s ο min ο hr Equivalence statement 15.2 π π π₯ 1 ππ 1000 π π₯ 60 π 1 πππ π₯ 60 πππ 1 βπ =54.7 ππ/βπ

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**Ex 13) Convert 0.510 in/ms to km/hr**

in ο cm ο m ο km; ms ο s ο min ο hr Equivalence statement 1 in = 2.54cm .510 ππ ππ π₯ 2.54ππ 1ππ π₯ 1π₯ 10 β2 π 1ππ π₯ 1ππ 1000π π₯ 1ππ 1π₯ 10 β3 π π₯ 60π 1πππ π₯ 60πππ 1βπ =46.6 ππ/βπ

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