Unit Conversions And the SI system
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.