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Lesson 1.06
Unit Conversion
System of Measurements
English System
Metric System
-Volume measured in
quarts, cups, gallons
-Mass measured in pounds
and ounces
System of
measures
- Volume measured in
liters
-Mass measured in grams
-Distance measured in
inches, yards, feet, miles
-Distance measured in
meters
-hard to convert form one
unit to another
-Easy to convert
Unit Conversions
• Dimensional Analysis:
-A problem-solving method used in physics,
chemistry, engineering, and mathematics
that is based on treating units in
calculations as algebraic factors or
fractions.
-A way to set up math problems; unit
conversions.
-Sets up multiplication and division in fraction
forms.
Steps in Unit conversion
Example: How many minutes are in 2 days?
1)What are you looking for?
• What unit do you want to have for your
answer? This is usually given in the
problem or question being asked.
- 2 days and number of minutes
2) What do you already know?
• What equalities or conversions do you
already know that might help you solve the
Steps
problem? Don’t forget that you know the
metric prefixes and their relationship to
each base unit.
• Each step in the setup is its own
conversion. The numerator must be equal
to the denominator.
- 1 day = 24 hours; 1hour = 60 minutes
3) Where does the information go?
• Start with the given amount and its unit
Steps
and use equalities until all the units cancel
except the unit you need for your final
answer.
• Every equivalent can be flipped(1 hr/60
mins or 60 mins/ 1 hr)—be sure to keep
each number with its correct unit, but you
can switch which one is in the numerator
and which one is in the denominator.
- 2 days x 24 hrs/1 day x 60 mins/ 1 hr
Steps
4) Solve it!
• You multiply everything that is on top
(numerators).
• Then divide by everything that is on the
bottom (denominators) to get the number
that goes in your answer.
- Numerator(top) = 2 x 24 x 60 = 2880
Denominator (bottom)= 1 x 1 = 1
- 2880/1 = 2880 minutes
Sample Problem
A)If your dog weighs 40 kilograms, how many
milligrams does it weigh?
Step 1- 40 kg and number of milligrams(mg)
Step 2- 1 kg = 10^3 g ; 10^-3g = 1 mg
Step 3- 40 kg x 10^3 g/1 kg x 1 mg/10^-3 g
Step 4- (top)40 x 10^3 x 1 = 40000
(bottom)1 x 10^-3 = 0.001
40000/0.001 = 40,000,000 mg
Sample Problem
B)Change the measurement 150 mm to dam
Step 1 -150 mm and unit dam
Step 2 - 1 mm = 10^-3 m ; 1 dam = 10^1 m
Step 3 - 150 mm x 10^-3 m/1mm x 1 dam/
10^1 m
Step 4 - 150 x 10^-3 x 1 / 1 / 10^1
= 0.015 dam
Sample Problem
C) Convert 6.5 cm/s to m/hr(unit is a fraction)
Step 1- 6.5 cm/s and m/hr
Step 2-1 m = 100 cm ; 1 hr = 60 mins ;
1 min = 60 secs
Step 3- (convert numerator first) 6.5 cm/s x
1 m/100 cm = 0.065
- you can start with the numerator first. The
one sec is still in the denominator, but you
can ignore it until you get cm converted to
m.
Sample Problems
- now you can continue the problem by
changing the denominator from s to hr.
(convert denominator) 0.065 m/s x 60 s/1
min x 60 min/1 hr
Step 4 – (top)0.065 x 60 x 60 = 234
(bottom) 1 x 1 = 1
234 / 1 = 234 m/hr
Sample Problem
D) Convert the density 6.2 g/mL to kg/L
Step 1 - 6.2 g/mL and unit kg/L
Step 2 – 1000 g = 1 kg ; 1 L = 1000 mL
Step 3 – 6.2 g/mL x 1kg/1000 g x 1000 mL/
1L
Step 4 – 6.2 x 1 x 1000 / 1000 / 1
= 6.2 kg/L
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