Converting Units

Converting Units

Likely the most useful thing you will learn all year.

Lecture Part A. (Just watch and think)A sign along the road in Canada

says “100 kilometers/hour.” What is this in miles per hour?

€

100 kmhour

€

100 kmhour

€

mileshour=

€

100 kmhour

×

€

mileshour=

€

100 kmhour

× miles

km

€

mileshour=

Metric1 meter =100 cm

1 kilometer = 1000 meters1centimeter = 10 millimeters

1 kilogram = 1000 grams

Metric and US1 inch = 2.54 cm

1 kilogram = 2.2 pounds1 mile = 1.61 kilometers

US1 foot = 12 inches1 mile = 5280 feet

1 yard = 3 feet

€

100 kmhour

× miles

km

€

mileshour

1.61 km = 1 mile&

1 km = 0.621 miles

=

€

100 km

hour×

1 miles

1.61 km

€

mileshour

1.61 km = 1 mile&

1 km = 0.621 miles

=

=

€

62.14 mileshour

€

100 km

hour×

1 miles

1.61 km

Lecture Part B. (Just watch and think)

An airplane has a speed of 600 miles per hour.

How fast is this inmiles per minute?

€

600 mileshour

€

600 mileshour

=

€

miles

minute

€

600 mileshour

×

=

€

miles

minute

€

600 mileshour

× hour

minute =

€

miles

minute

€

600 mileshour

× hour

minute =

€

miles

minute

1 hour = 60 minutes

€

600 mileshour

×1 hour

60 minute =

€

miles

minute

1 hour = 60 minutes

€

600 mileshour

×1 hour

60 minute =

€

10 miles

minute

10 miles/min is the samespeed as 600 miles/hour

€

600 mileshour

×1 hour

60 minute =

€

10 miles

minute

Wait a tick…Why does this method work?

x ÷ x = ?

x ÷ x = ?

€

1 hour

60 minutes= ?

x ÷ x = ?

€

1 hour

60 minutes= 1

€

600 mileshour

×1 hour

60 minute =

€

10 miles

minute

This method works because when youmultiply by 1 you do not change the

value of the quantity.

1a. The piece of paper on your desk is 81/2 inches by 11 inches.

In centimeters, how wide is the page?

€

8.5 inches

€

8.50 inches = cm

€

8.5 inches × cm inches

= cm

€


How many centimeters equals how many inches?

= cm







1 yard = 3 feet

€


2.54 centimeters = 1 inch

= cm

€

8.5 inches ×2.54 cm1 inch

= cm

2.54 centimeters = 1 inch

€

8.5 inches ×2.54 cm1 inch

= 21.6 cm

The piece of paper is 21.6 cm wide.

1b. What is the width of the page, in feet?

What is the width of the page,in feet?

What should we start with:

8.50 inches, or 21.6 cm?

€

8.5 inches

€

8.5 inches = ft

€

8.5 inches ×

= ft

€

8.5 inches × ft

inches= ft

€

8.5 inches × ft

inches

How many feet equals how many inches?

= ft







1 yard = 3 feet

1 foot = 12 inches

= ft

€

8.5 inches × ft

inches

€

8.5 inches ×1 ft

12 inches= ft

1 foot = 12 inches

€

8.5 inches ×1 ft

12 inch= ft

= 0.708 ft

€

8.50 inches ×1 ft

12.0 inch

The page is 0.708 feet long

2a. A football field is 100 yards.How many inches is this?

€

100 yards = inches

€

100 yards× ft

yard×

inches foot = inches

€

100 yards×3 ft

1 yard×

12 inches1 foot = inches

€

100 yards×3 ft

1 yard×

12 inches1 foot = 3600 inches

2b. How many kilometers long is a football field?

€

3600 inches = km

€

3600 inches × cm

inch×

meter cm

× km m

= km

€

3600 inches ×2.54 cm1 inch

×1 meter100 cm

×1 km

1000 m

= km

€

3600 inches ×2.54 cm1 inch

×1 meter100 cm

×1 km

1000 m

= 0.09144 km

2c.Looking for some extra practice?How long is a football field in:

• Miles

• Meters

• Inches

• Centimeters

2c. Answers:

• Miles [0.057]

• Meters [91.44]

• Inches [3600]

• Centimeters [9144]

3. A student is 17 years old.How many hours old is the student?

€

17 years =

€

17 years = hours

€

17 years× days

years= hours

€

17 years× days

years×

hours days

= hours

€

17 years×365 days1 year

× hours days

= hours

€


×24 hours

1 day= hours

€


×24 hours

1 day= 148,920 hours

4. A sprinter is running at 10 m/s. How fast is this, in miles per hour?

€

10 m

s

miles= per

hour

€

10 m

s

€

10 m

s×

km

m×

mile

km×

s

min×

min

hour

miles= per

hour







1 yard = 3 feet

€

10 m

s×

1 km

1000 m×

1 mile

1.61 km×

60 s

1 min×

60 min

1 hour

miles= per

hour

€

10 m

s×

1 km

1000 m×

1 mile

1.61 km×

60 s

1 min×

60 min

1 hour

miles

= 22 per

hour

5. A hotel room in Paris is 110 Euros.

How much is this in US Dollars?

€110

€110 = $

€110 = $

€

Dollars Euros

1 Euro = 1.4 Dollars1 Dollar = 0.72 Euros

€110 = $

€

Dollars Euros


€110 = $

€

1.4 Dollars1.0 Euros


€110 = $ 154

€

1.4 Dollars1.0 Euros

6a. A shoe box is5 inches x 3 inches x 11 inches

= 165 cubic inches.How many cubic centimeters is this?

€

165 in.3 =165 inches ⋅inches ⋅inches

€

165 in.3 = cm3

€

165 in.3 ×2.54 cm1 inch

×2.54 cm1 inch

×2.54 cm1 inch

= cm3

€

165 in.3 ×2.54 cm1 inch

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

= cm3

€

165 in.3 ×2.54 cm1 inch

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

= 2700 cm3

6b. Extra practice:Your desktop is about

200 square inches.What is this area in square feet

and square centimenters?

Answers. The area of your desktop is:

• 1.38 ft2

• 1,290 cm2

7. The density of water is exactly 1 g/cm3. What is the density of water in pounds per cubic foot?

€

1 g cm3 = pounds per cubic foot







1 yard = 3 feet

€

1 g

cm3 × kg g

× lb kg

× cm

inch

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

× inches foot

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

= pounds per cubic foot

€

1 g cm3 ×

1 kg 1000 g

× 2.2 lb1 kg

×2.54 cm1 inch

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

×12 inches

1 foot

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

= pounds per cubic foot

€

1 g cm3 ×

1 kg 1000 g

× 2.2 lb1 kg

×2.54 cm1 inch

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

×12 inches

1 foot

⎛ ⎝ ⎜

⎞ ⎠ ⎟3

= 62 pounds per cubic foot

8. A truck can unload 100 kg of stone in 2 minutes. How fast is

this, in pounds per second?

€

100 kg2 min

= pounds / second

€

100 kg2 min

× lb kg

× min sec

= pounds / second







1 yard = 3 feet

€

100 kg2 min

×2.2 lb1 kg

×1 min60 sec

= pounds / second

€

100 kg2 min

×2.2 lb1 kg

×1 min60 sec

= 1.8 pounds / second

9. A landscaper can move 2 kgof soil every minute.

How many hours will it take to move 300 pounds?

€

300 lb

€

300 lb = hours

= hours

€

300 lb • kg

lb•

min

kg•

hr

min

= hours

€

300 lb • kg

lb•

20 min

40 kg•

hr

min

= hours

€

300 lb •1 kg

2.2 lb•

20 min

40 kg•

1 hr

60 min

= 1.1 hours

€

300 lb •1 kg

2.2 lb•

20 min

40 kg•

1 hr

60 min

Estimating

≈

Which is greater:

A. The number of pieces of printer paper, stacked from floor to ceiling.

B. The number of walking steps from the High School to the Middle School.

C. They are about the same.

How could we estimate option A.?

About how far is it from the floor to the ceiling?

How tall is a package of paper?

€

feet ⋅ inches

ft.⋅ pckg paper

inches⋅

sheets1 pckg paper = sheets

€

9 feet ⋅12 inches

1 ft.⋅1 pckg paper

2 inches⋅

500 sheets1 pckg paper

= sheets

€

9 feet ⋅12 inches

1 ft.⋅1 pckg paper

2 inches⋅

500 sheets1 pckg paper

= 27,000 sheets

About how far away is the middle school?

About how big is one step?

€

miles ⋅ feet mile

⋅ step feet

= steps

€

2 miles ⋅5280 feet

1 mile⋅1 step3 feet

= steps

€



= 3,520 steps

€



= 3,520 steps

btw, 27,000 steps ≈ distancefrom here to Solon, OH

Which is greater:

A. The number of pieces of printer paper, stacked from floor to ceiling.

B. The number of walking steps from the High School to the Middle School.

C. They are about the same.

E1a. Estimate how many hours a McDonald’s worker must work to earn enough to buy a car. Assume that all

the money goes toward the car.

$

How much is a car?

What is the wage of a McDonald’s worker?

€

$ ⋅ hour$ = hours

€

$7,000 ⋅1 hour$ 7.00 = hours

€

$7,000 ⋅1 hour$ 7.00 = 1000 hours

E1b. How many years is this?

€

1000 hours ⋅ week hours

⋅ year

weeks= years

€

1000 hours ⋅1 week40 hours

⋅1 year

52 weeks= years

€

$1000 hours ⋅1 week40 hours

⋅1 year

52 weeks= 0.48 years

E2. If you drove from here to San Francisco, about how many times

would you stop for gas?

How far away is San Francisco?

How far can you drive on one tank of gas?

How far can you drive on one gallon of gas?

How many gallons fit in a tank?

€

miles ⋅ gallon miles

⋅ tank

gallons = tanks

€

2500 miles ⋅1 gallon30 miles

⋅1 tank

10 gallons = tanks

€

2500 miles ⋅1 gallon30 miles

⋅1 tank

10 gallons = 8 tanks

E3. If you wanted to buy sliced turkey to feed the entire senior class,

how much would that cost?

How many students is that?

How much does each student need?

What is the cost, per pound?

€

students ⋅ pound student

⋅$

pound = $

€

400 students ⋅1

4 pound

1 student⋅

$ 51 pound

= $

= $ 500

€

400 students ⋅1

4 pound

1 student⋅

$ 51 pound

E4a. About how many hours have you spent in school?

How many years have you been in school?

How many days in a year?

How many hours in a day?

€

years ⋅ days year

⋅ hours day = hours

€

12 years ⋅180 days

1 year⋅7 hours1 day = hours

€


1 year⋅7 hours1 day = 15,000 hours

E4b. About what percentage of your life have you spent in school?

%

How many hours old are you?

€

17 years ⋅365 days1 year

⋅24 hours

1 day = 150,000 hours

€

15,000 hours in school150,000 hours old

⋅100% =10%

E4c.What percentage of your waking life have you spent in school?

How many hours are you awake every day?

€


1 year⋅16 hours

1 day = hours

€


1 year⋅16 hours

1 day = 99,000 hours

€

15,000 hours in school99,000 hours old

⋅100% =15%

Converting Units

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