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 2.54𝑐𝑚
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
2.85𝑐𝑚 𝑥 1𝑖𝑛 2.54𝑐𝑚 = 2.85𝑖𝑛 2.54 =1.12𝑖𝑛

4. 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

5. 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

6. 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

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 𝑥 2.54𝑐𝑚 1𝑖𝑛 =7𝑥2.54𝑐𝑚=64.8𝑐𝑚

8. 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

9. 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

10. 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

11. 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

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 𝑥 1000𝑚 1𝑘𝑚 𝑥 𝑦𝑑 1𝑚 𝑥 1𝑚𝑖 1760𝑦𝑑 =6.22 𝑚𝑖

13. 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

14. 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

15. Ex 7) The average speed of a nitrogen molecule in air at 25C 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

16. 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

17. 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

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  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

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  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

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  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

21. 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