Download How to Solve Metric Conversion Problems

How to Solve Metric Conversion Problems
Sample Problem 10 cg = ________ g
This question is basically asking how many micrograms (mg) are in 10 centigrams (cg) and can be
solved in two simple steps:
(1) First, determine the “power of 10” difference between the two metric values- (this requires
learning all of the metric prefixes and their associated power of 10—see back page of handout)
A centigram is equal to 10-2 grams
A microgram is equal to 10-6 grams
The difference = 104
-2
-6
-3
-4
-5
-6
(because there are four “powers of 10” between 10 to 10 (ie) 10 , 10 , 10 10 )
(2) Second, determine whether to multiply (when known is bigger than unknown) or divide (when
known is smaller than unknown) the known value by the power of 10 difference determined in part (1).
10 cg = __ g
Known
Unknown
In this case the KNOWN (cg) is BIGGER than the unknown (g) therefore we will MULTIPLY the known value
by the power of 10 difference:
ANSWER: 10 cg x 104 = 105 g
In answer to the above question, there are 105 micrograms (mg) in 10 centigrams (cg).
(Reminder: How to multiply exponents  103 x 106 = 109 or 10 x 104 = 105 because “10” is the same as 101)
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Solving Reverse Problem ____ cg = 10 g
4
(1) The power of 10 difference is same as original question above 10 ( b/c centi 10-2 micro 10-6)
__cg
= 10 g
Unknown Known
(2) This time the KNOWN (g) is SMALLER than unknown(cg) so will DIVIDE the known by the power of
10 difference from part (1)
ANSWER : 10 g/ 104 = 1/103 cg (or 1 x 10-3 cg)
Created by Kelly J Cude, Ph.D. for College of the Canyons June 2012
Metric Prefixes and Power of 10 Values (from lab notebook)
PREFIX
ABBRIVIATION
DECIMAL EQUIVALENT
EXPONETIAL EQUIVALENT
-12
Pico
p
0.000000000001
10
Nano
n
0.000000001
10
Micro

0.000001
10
Milli
m
0.001
10
Centi
c
0.01
10
Deci
d
0.1
10
1.0
10
No prefix
-9
-6
-3
-2
-1
-0
3
Kilo
k
1000.0
10
Mega
M
1,000,000.0
10
Giga
G
1,000,000,000.0
10
6
Solve the following practice problems: (L- liters, m –meters, g-grams)
(1) 100mL = _______L
(2) 5dg= _______g
(3) _______m = 2km
(4) _______ cg = 10g
(5) 20 L = ______L
Created by Kelly J Cude, Ph.D. for College of the Canyons June 2012
9
How to Solve Dimensional Analysis Problems
Sample Problem: How many seconds are in 4 days?
(1) First, determine the conversion factors that will help you to change from the given units (hours) to
the desired units (seconds). The conversion factors below will be useful:
60 sec ;
1 min
60 min
1 hr
;
24 hr
1 day
(2) Second, multiply your given value by the conversion factors such that all of the unwanted units
“cancel out” and you are left with the desired units in your answer.
ANSWER: 4 days x 24 hr x 60 min x 60 sec = 345,600 sec
1 day 1 hr
1 min
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Sample Problem: You are given a bottle of Drug X (containing pills that are 0.5 grams),
and asked by the doctor to administer a total of 6000 mg to your patient. How many
pills should you give the patient?
(1) useful conversion factors (reminder “milli” = 10-3)
1 pill
;
1g
0.5 g
1000mg
(2) multiply given by conversion factors to cancel out unwanted units.
ANSWER:
6000mg
x 1 gram x 1 pill = 12 pills
1000mg 0.5 g
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Solve the following practice problems
(1) If an inch is 2.54 centimeters, how long is a foot-long sandwich from Subway in centimeters?
(2) If a kilogram is 2.2 pounds, how many grams are in 10 pounds?
(3) If 1 cc (cubic centimeter) = 1 mL (milliliter), how man cc’s are in 0.5 L of saline solution?
Created by Kelly J Cude, Ph.D. for College of the Canyons June 2012
Working with Exponents and Scientific Notation (10X)
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For
example, instead of writing 0.000000085, we write 8.5 x 10-8. Instead of writing 59, we write 5.9 X 101 Let’s see
how this works.
Sample Problem, what is the scientific notation for 0.0000000056?
(1) first determine the digit term = the whole number
For 0.0000000056, the digit term = 5.6
(2) determine the exponential term. The exponent of 10 is the number of places the decimal point must be
shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that
number of places to the right (very large number). A negative exponent shows that the decimal point is shifted
that number of places to the left (a very small number).
For 0.0000000056, the exponential term = 10-9
ANSWER:
For the final answer, multiple the product of the two numbers: 5.6 (the digit term) and 10-9 (the exponential
term) = 5.6 x 10-9
Rules for Multiplying and Dividing numbers in Scientific Notation (exponents)
 When multiplying numbers containing exponents, the digit terms are multiplied normally, while the
exponent values are added together.
Example: 2 x105 (x) 3 x 102
Solve for whole numbers: 2 (x) 3 = 6 AND solve for exponents : 105 (x) 102 = 107
Answer: multiply together = 6 x 107
 When performing division with numbers containing exponents, the digit terms are divided normally, while
the exponent values are subtracted from one another.
Example: 6 x 107
3 x 105
Solve for whole numbers: 6/3 = 2 AND solve for exponents: 107/ 105 = 102
Answer: multiply together 2 x 102
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Solve the Following Practice Problems
(1) What is the scientific notation for 0.000067? for 45, 000?
(2) 85000 x 3600 = __________. Give your answer in scientific notation
(3) 0.00045 = ___________. Give your answer in scientific notation
000.22
(4) (4.5 x 10-14) x (5.2 x 103)= _______________. Give your answer in scientific notation
Created by Kelly J Cude, Ph.D. for College of the Canyons June 2012