Do Now:
1)Nick spent $300 for 5 ps3 video games. How much would the
customer have spent if he bought 2 video games?
2) Alexis took 10 hours to read a 300 page book. At this rate, how long
will it take her to read a 900 page book?
Homework Questions
Kilo = 1000
Deci = one-tenth 1/10
Centi = one-hundredth 1/100
Milli = one-thousandth 1/1000
Metric System
1 kilometer (km) = 1000 meter (m)
1 centimeter (cm) = .01 meter
1 millimeter (mm) = .001 meter
1 kilogram(kg) = 1000 grams (g)
1 miligram (mg) = .001 gram (g)
1 milliter = .001 liter
English System of
Measurement
12 inches (in) = 1 foot (ft)
3 feet = 1 yard (yd)
5280 feet = 1 mile (mi)
16 ounces (oz) = 1 pound (lb)
2000lb = 1 ton
Do not copy
3 teaspoons (tsp) = 1 tablespoon (tbsp)
16 tbsp = 1 cup (c)
8 ounces (oz) = 1 c
2 c = 1 pint (pt)
2 pt = 1 quart (qt)
4 qt = 1 gallon (gal)
Conversions and Proportions
To convert from one unit to another, you
multiply the original unit by a
conversion factor that produces the
desired unit.
 A conversion factor is a ratio of two
equivalent measures in different units.

Procedure
When converting measurements,
1. Use the appropriate conversion
factors
2. Divide common units
3. Simplify.
Example 1
Convert 1.245 kilometers to meters.
1.245 km
𝟏𝟎𝟎𝟎 𝒎𝒆𝒕𝒆𝒓𝒔
●
𝟏 𝒌𝒎
Example 2
Convert 330 min to hours.
Example 3
Convert 5 ft 3 inches into inches
5ft 3 inches = 5 ft + 3 inches
Practice!
Convert the given amount to the given unit.
1) 63 yd; feet
2) 200cm; meters
3) 2.5 lbs; ounces
4) 4 mins; seconds
5) Find the mistake:
9yd = ? Ft
9yd ×
3𝑦𝑑
1𝑓𝑡
=27 ft
Oct. 11
Aim: How do we convert rates?
Why do we convert units?
Do Now: Convert 20 grams into kilograms
What are we given?
20 grams
What do we want? Kilograms
What do we know? 1 kg = 1000 grams
20 grams into kilograms
We want to change it into kilograms:
1. Use appropriate conversion factor.
20 grams x (conversion factor)
20 grams x (
20 g x
(
𝑘𝑔
)
𝑔
𝑔𝑟𝑎𝑚𝑠
)
20 g x (
𝑘𝑔
)
𝑔
We know 1 kg = 1000 g.
20 g x (
1 𝑘𝑔
)
1000 𝑔
2. Divide out/Cancel units
20 g x (
1 𝑘𝑔
)
1000 𝑔
20 x (
1 𝑘𝑔
)
1000
3. Simplify
20
1
x(
=
1 𝑘𝑔
)
1000
20(1𝑘𝑔)
1 (1000)
20𝑘𝑔
=
1000
= 0.02kg
Converting rates
The procedure is still the same!
Use appropriate conversion factors.
2. Divide common units
3. Simplify
1.
Example 1
A car is traveling 55mi/h. What is the car’s
speed in feet per minute?
55 mi/ h =
55 𝑚𝑖𝑙𝑒𝑠
1 ℎ𝑜𝑢𝑟
First let’s convert miles to feet!
We should know that 1 mile = 5280 ft
55 𝑚𝑖
x
1 ℎ𝑟
(
5280 𝑓𝑡
)
1 𝑚𝑖
55 𝑚𝑖𝑙𝑒𝑠
x
1 ℎ𝑜𝑢𝑟
(
5280 𝑓𝑡
)
1 𝑚𝑖
Before we divide out/ cancel units…
Let’s also multiply by the conversion factor
for hours to minutes.
55 𝑚𝑖𝑙𝑒𝑠
x
1 ℎ𝑜𝑢𝑟
(
5280 𝑓𝑡
)
1 𝑚𝑖
x(
)
Wait a minute…. Where should hours go?
55 𝑚𝑖𝑙𝑒𝑠
x
1 ℎ𝑜𝑢𝑟
55 𝑚𝑖
x
1 ℎ𝑟
(
(
5280 𝑓𝑡
)
1 𝑚𝑖
5280 𝑓𝑡
)
1 𝑚𝑖
x(
x(
ℎ𝑟
𝑚𝑖𝑛
)
)
We know all know that 1 hr = 60 minutes
55 𝑚𝑖
x
1 ℎ𝑟
5280 𝑓𝑡
)
1 𝑚𝑖
(
x(
1 ℎ𝑟
60 𝑚𝑖𝑛
2. Divide out/cancel units
55 𝑚𝑖
x
1 ℎ𝑟
(
5280 𝑓𝑡
)
1 𝑚𝑖
x(
1 ℎ𝑟
60 𝑚𝑖𝑛
)
)
55
x
1
5280 𝑓𝑡
1
(
) x ( 60 𝑚𝑖𝑛
1
55 ● 5280𝑓𝑡 ● 1
=(
)
1 ● 1● 60 𝑚𝑖𝑛
290,400 𝑓𝑡
=
60 𝑚𝑖𝑛
= 4,840
𝑓𝑡
𝑚𝑖𝑛
= 4,840 ft/min
)
A car is traveling 60 mi/h. What
is the car’s speed in feet per
minute?
Try this one by yourselves!
A car is traveling 60 mi/h. What
is the car’s speed in feet per
minute?
Try this one by yourselves!
60 mi/hr =
60 𝑚𝑖
1 ℎ𝑜𝑢𝑟
1. Use appropriate conversion factors!
60 𝑚𝑖
𝑓𝑒𝑒𝑡
ℎ𝑜𝑢𝑟
x(
)(
)
1 ℎ𝑜𝑢𝑟
𝑚𝑖
𝑚𝑖𝑛
60 𝑚𝑖
5280 𝑓𝑒𝑒𝑡
1 ℎ𝑜𝑢𝑟
x(
)(
)
1 ℎ𝑜𝑢𝑟
1 𝑚𝑖
60 𝑚𝑖𝑛
60 𝑚𝑖
1 ℎ𝑜𝑢𝑟
x(
5280 𝑓𝑒𝑒𝑡
1 ℎ𝑜𝑢𝑟
)(
)
1 𝑚𝑖
60 𝑚𝑖𝑛
2. Divide out/cancel units
60 𝑚𝑖
1 ℎ𝑜𝑢𝑟
x(
5280 𝑓𝑒𝑒𝑡
1 ℎ𝑜𝑢𝑟
)(
)
1 𝑚𝑖
60 𝑚𝑖𝑛
3. Simplify
60
1
x(
5280 𝑓𝑒𝑒𝑡
1
)(
)
1
60 𝑚𝑖𝑛
60 ● 5280 𝑓𝑡
=
1● 1● 60 𝑚𝑖𝑛
316,800 𝑓𝑡
=
60 𝑚𝑖𝑛
=
5,280 ft
𝑚𝑖𝑛
= 5280 ft/min
Practice! – Do not copy
1) A car is traveling 45
mi/h. What is the car’s
speed in feet per
minute?
When you are done, do
2) 50 miles per hour to feet
per second
3) A cheetah ran 300 ft in
2.92 seconds. What was the
cheetah’s average speed in
miles per hour?
4) Jason ran the 50-yd dash
in 5.8 seconds. At what
speed did Jason run in ft
per min? Round to the
nearest tenth!
1) A car is traveling 45 mi/h. What is the
car’s speed in feet per minute?
1)
2)
3)
45 𝑚𝑖
5280 𝑓𝑡
x(
1 ℎ𝑟
1 𝑚𝑖
45 𝑚𝑖
5280 𝑓𝑡
x(
1 ℎ𝑟
1 𝑚𝑖
45 (5280𝑓𝑡)(1)
1 (1)(60 min)
=
237600 𝑓𝑡
60 𝑚𝑖𝑛
= 3,960 ft/min
)x
)x
1 ℎ𝑟
(
)
60 𝑚𝑖𝑛
1 ℎ𝑟
(
)
60 𝑚𝑖𝑛
50 miles per hour to feet per second
50 𝑚𝑖
1 ℎ𝑟
What are the conversion factors?
50 𝑚𝑖
1 ℎ𝑟
5280 𝑓𝑡
1 ℎ𝑟
(
)(
)
1 𝑚𝑖
60 𝑚𝑖𝑛
50 5280 𝑓𝑡 (1)
1 1 (60 min)
264,000 𝑓𝑡
60 𝑚𝑖𝑛
4,400 ft/min
Problem 3-A cheetah ran 300 ft in 2.92 seconds. What
was the cheetah’s average speed in miles per hour?
Use conversion factors
300 𝑓𝑡
2.92𝑠
x
1 𝑚𝑖
5280 𝑓𝑡
x
60 𝑠
1 𝑚𝑖𝑛
x
60 𝑚𝑖𝑛
1 ℎ𝑟
300 1 𝑚𝑖 (60)
2.92(5280)(1)(1ℎ𝑟)
=
18,000 𝑚𝑖
15,417.6 ℎ𝑟
= 1.167 mi/hr
Problem 4
Jason ran the 50-yd dash in 5.8 seconds. At what
speed did Jason run in ft per min?
50 yards in 5.8 seconds = 50 yards/sec
50𝑦𝑑
3 𝑓𝑡 60 𝑠
x(
)(1 𝑚𝑖𝑛)
5.8 𝑠
1 𝑦𝑑
=
50 (3𝑓𝑡)
5.8 (1 min)
=
150 𝑓𝑡
5.8 𝑚𝑖𝑛
= 25.86207 ft/min ≈ 25.9 ft/min
Exit Slip – Round to nearest
tenth.
1)
2)
16 meters per second to centimeters
per minute
40 kilometers per hour to meters per
second
Extra Practice
Convert 2.2kg into lbs. Use the fact that 1lb
= 0.45kg.