Unit Conversions

And the SI system

Unit Conversion

• Conversions are part of daily life

Hours worked → $ on paycheck

Travel distance → Minutes of driving

Kind of cell phone → Cost of calling plan

Unit Conversion

• Both things are equivalent, but you change them in order to make better sense of the information.

• Def: Conversion- changing a number from one kind of unit to another in order to use it in an equation.

Why convert?

• In physics we take basic measurements of time, mass, and length all the time.

• Before we can do ANY math, these measurements HAVE to be in these SI units:

Time- seconds (s)Mass- kilogram (kg)Length- meter (m)

Common Conversions

• Time:1 min = 60 s1 hr = 3600 s1 day = 86,400 s

• Mass:2.2 lb = 1kg

• Length:1 in = 2.54 cm1 mi = 5280 ft

How do we convert?

• Another way to write that two things are equivalent is to write them as a fraction.

• Example:

1 in = 2.54 cm is the same as

and alsocm

in

54.2

1

in

cm

1

54.2

Conversion Factors

• Writing an equivalency like this is called a Conversion Factor.

• This is what we use to go from one unit to another.

cm

in

54.2

1

in

cm

1

54.2

Conversion Factors• Any of these can be written as conversion factors. (It doesn’t matter which

number is on the top and which is on the bottom)

1 min = 60 s or

1 hr = 3600 s or

1 day = 86,400 s or

2.2 lb = 1kg or

1 in = 2.54 cm or

1 mi = 5280 ft orft

mi

cm

in

kg

lb

s

day

s

hr

s

5280

1

54.2

1

1

2.2

86400

1

3600

1

60

min1

mi

ft

in

cm

lb

kg

day

s

hr

s

s

1

5280

1

54.2

2.2

1

1

86400

1

3600

min1

60

Using Conversion Factors

• Example: Convert 5 in to centimeters.

• Step 1: Write the number down WITH UNITS.

5 in

Using Conversion Factors

• Example: Convert 5 in to centimeters.

• Step 2: Set up a “T chart”.

5 in

Using Conversion Factors

• Example: Convert 5 in to centimeters.

• Step 3: Find a conversion factor with the same units IN THE DENOMINATOR.

5 in 2.54cm 1 in

Using Conversion Factors

• Example: Convert 5 in to centimeters.

• Step 4: Cancel units (NOT numbers)

5 in 2.54cm 1 in

=

Using Conversion Factors

• Example: Convert 5 in to centimeters.

• Step 5: Simplify and keep the units that AREN’T cancelled out

5 in 2.54cm 5 * 2.54 cm 12.7 cm

1 in 1

= =

Practice

• On a scratch piece of paper, perform the following conversions:

• Convert 3 days into seconds.

• Convert 600 feet into miles.

• Convert 195lbs into kilograms.

Practice

• On a scratch piece of paper, perform the following conversions:

• Convert 3 days into seconds.259,200s

• Convert 600 feet into miles.

• Convert 195lbs into kilograms.

Practice

• On a scratch piece of paper, perform the following conversions:

• Convert 3 days into seconds.259,200s

• Convert 600 feet into miles.0.11 mi

• Convert 195lbs into kilograms.

Practice

• On a scratch piece of paper, perform the following conversions:

• Convert 3 days into seconds.259,200s

• Convert 600 feet into miles.0.11 mi

• Convert 195lbs into kilograms.88.63 kg

Two Step Conversions

• Some conversions may require two conversion factors to complete.

• Example: Convert 1 mi into inches.

1mi

Two Step Conversions

• Some conversions may require two conversion factors to complete.

• Example: Convert 1 mi into inches.

1mi 5280ft 1mi

Two Step Conversions

• Some conversions may require two conversion factors to complete.

• Example: Convert 1 mi into inches.

1mi 5280ft 12in 1mi 1ft

Two Step Conversions

• Some conversions may require two conversion factors to complete.

• Example: Convert 1 mi into inches.

1mi 5280ft 12in 1*5280*12 in 1mi 1ft 1*1

=

Two Step Conversions

• Some conversions may require two conversion factors to complete.

• Example: Convert 1 mi into inches.

1mi 5280ft 12in 1*5280*12 in 63,360 in 1mi 1ft 1*1

= =

Practice

• Perform the following conversion:

• Convert .5 years to seconds.

• Convert 1 ton to kilograms (1 ton is 2000 lbs).

Practice

• Perform the following conversion:

• Convert .5 years to seconds.15,768,000 s

• Convert 1 ton to kilograms (1 ton is 2000 lbs).

Practice

• Perform the following conversion:

• Convert .5 years to seconds.15,768,000 s

• Convert 1 ton to kilograms (1 ton is 2000 lbs).909.1 kg

SI Prefixes

• These are some common prefixes to the SI units that can help you come up with more conversion factors:

• Centi: 1/100th

Ex: 100 cm = 1 m• Milli: 1/1000th

Ex: 1000 ms = 1 s• Kilo: 1000

Ex: 1 kg = 1000 g

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft h 1mi

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in h 1mi 1ft

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in 2.54cm h 1mi 1ft 1in

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in 2.54cm 1m h 1mi 1ft 1in 100cm

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in 2.54cm 1m 1h h 1mi 1ft 1in 100cm 3600s

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in 2.54cm 1m 1h h 1mi 1ft 1in 100cm 3600s

10*5280*12*2.54*1*1 m 1,609,344 m 1*1*1*100*3600 s 360,000 s

= =

Converting Multi Units

• Sometimes we have to convert two thing in one problem before doing the math.

• Example: Convert 10 mph into m/s.10 mi 5280ft 12in 2.54cm 1m 1h h 1mi 1ft 1in 100cm 3600s

10*5280*12*2.54*1*1 m 1,609,344 m 4.47m/s 1*1*1*100*3600 s 360,000 s

= = =

Practice

• Using your notes as a guide, complete the classwork assignment on unit conversion.