Physics Lesson 01
Converting Between Units
Before we get started:
• Think about when you’re cooking from a
recipe.
How do you
know how
much of
each
ingredient
you are
going to
use?
All recipes
give you both
a NUMBER
and a UNIT.
• If you use the wrong unit (teaspoons
instead of tablespoons), you mess up the
recipe.
• The same is true in physics: If you use the
wrong unit, you mess up the calculation.
Why do we use the units we do?
• The simple answer is: we pick the units that
are EASIEST for us to work with.
– You would never measure the amount of
gasoline that fills your car in teaspoons…that
would take forever. Instead, we use gallons.
– You would never measure the distance between
NY and LA in inches!
• In order to communicate scientifically with
people all over the world, we use SI Units
SI Units
• This stands for “Système International
d'Unités” or in English, the International
System.
• All scientists around the world communicate
using these units:
– DISTANCE is measured in METERS. (m)
– MASS is measured in KILOGRAMS. (kg)
– TIME is measured in SECONDS. (s)
– There are even more SI units, but we will get to
them in later chapters.
What do we do if the units we are given are
DIFFERENT than the ones we are WANT?
• We convert!
• There are 5 easy steps to converting.
1. IDENTIFY the units we are GIVEN.
2. IDENTIFY the units we WANT.
3. PICK the CONVERSION FACTORS to go from one
unit to the other.
4. DRAW a T-CHART and PLUG IN the conversion
factors.
5. CANCEL OUT units that show up on both the
BOTTOM and TOP. Then just do the math.
EXAMPLE:
• Erick lives 2.4 miles away from school, and Mr.
Brown challenged him to figure out how many
feet that was. Help him solve the problem.
• Step 1: IDENTIFY the units we are GIVEN.
“Erick lives 2.4 miles away from school.”
• Step 2: IDENTIFY the units we WANT.
“figure out how many feet that was”
EXAMPLE:
• Erick lives 2.4 miles away from school, and Mr.
Brown challenged him to figure out how many
feet that was. Help him solve the problem.
• Step 3: PICK the CONVERSION FACTORS to
go from one unit to the other.
Ask yourself, “How are miles related to feet?”
• You can find this information in charts, in
textbooks, and on the internet.
1 mile = 5280 feet
EXAMPLE:
• Erick lives 2.4 miles away from school, and Mr.
Brown challenged him to figure out how many
feet that was. Help him solve the problem.
• Step 4: DRAW a T-CHART and PLUG IN
the conversion factors.
We always start by putting We then always write the
the units we are GIVEN here. units we WANT to get here.
We will leave this box empty
for now. In later examples
we will use it.
EXAMPLE:
• Erick lives 2.4 miles away from school, and Mr.
Brown challenged him to figure out how many
feet that was. Help him solve the problem.
• Step 4: DRAW a T-CHART and PLUG IN
the conversion factors.
2.4 MILES
5280 FEET
1 MILE
EXAMPLE:
• Erick lives 2.4 miles away from school, and Mr.
Brown challenged him to figure out how many
feet that was. Help him solve the problem.
• Step 5: CANCEL OUT units that show up on
both the BOTTOM and TOP. Then just do
the math.
2.4 MILES
5280 FEET
1 MILE
= 12672 FEET
Doing the Math
• The math in physics is exactly the same as
the math you’ve done in your math classes.
• Look at the T-CHART like 2 fractions right
next to each other.
– If there are two numbers on the TOP, MULTIPLY
them.
– If there are two numbers on the BOTTOM,
MULTIPLY them.
– If there is one number on TOP and one on
BOTTOM, DIVIDE them.
Multi-Step Conversions
• Not all conversions will be simple enough to do in
just one step.
• The 5 rules for converting are still the same, you
will just need to use more conversion factors.
• For example, what if Mr. Brown had asked Erick
to convert his distance from miles to inches? What
would Erick do?
Solving Multi-Step Conversions
• There are two ways to solve multi-step
conversions:
1. You can solve one conversion, get the
answer, and then plug it into the next
conversion as your given.
2. You could draw one long T-Chart and use
many conversion factors at once.
**Both of them are equally correct. CHOOSE
the one that YOU feel COMFORTABLE with!
EXAMPLE:
• Let’s figure out how many inches away from
school Erick’s house is. Steps 1-3 are the
same, no matter which way you solve it.
– Step 1: Erick lives 2.4 miles from school.
– Step 2: How many inches away does Erick live?
– Step 3: 1 mile = 5280 feet
1 foot = 12 inches
EXAMPLE:
• Method 1: Solve, plug, solve
2.4 MILES
5280 FEET
= 12672 FEET
1 MILE
12672 FEET
12 INCHES
1 FOOT
= 152064 INCHES
EXAMPLE:
• Method 2: One big conversion
2.4 MILES 5280 FEET 12 INCHES
1 MILE
1 FOOT
= 152064 INCHES