Transcript Dimensional Analysis

Dimensional Analysis/Metric
Conversion
English-Standard Systems
There are two common systems of standardized units used for measurement
1.) English-inches (in), feet (ft), yards (yd), and miles (mi)
2.) Metric system-millimeters (mm), centimeters (cm), meters (m), and kilometers
(km)
*The United States is the only country in the world to use the English system
*Scientists use metric system
Metric System
The names of units in the metric system use prefixes that are based on powers of ten
Prefix
Meaning
Giga (G)
1 billion 1,000,000,000X
Mega M)
1 million 1,000,000X
Kilo (k)
1 thousand 1,000X
Hecto (H)
1 hundred 100X
Deca (D)
1 ten 10X
Deci (d)
1 tenth 0.1X
Centi (c)
1 onehundredth 0.01X
Milli (m)
1 onethousandth 0.001X
Micro μ)
1 onemillionth 0.000001X
6 city blocks
height of a 1st grader
Width of Pencil tip
Width of pinky
1km
1m
1cm
1mm
Distance, Volume, Mass, Time
There are 4 main areas of measurement:
1.) distance
3.) mass
2.) volume
4.) time
Distance-measures how far from one point to another
-base unit is meter (m)
Volume-measures the amount of space an object takes up
-base unit is liter (L)
Mass-measures amount of matter in an object
-base unit is grams (g)
Time-The measure of durations of events and the intervals between them
-base unit is second (s)
Metric System Prefixes
Write the name of the metric system abbreviation:
1.) mg=_________________
6.) L=_________________
2.) mm=________________
7.) m=_________________
3.) HL=_________________
8.) km=________________
4.) dL=_________________
9.) mg=________________
5.) ms=_________________
10.) g=_________________
Dimensional Analysis
Dimensional analysis is a method of conversion
that is applicable with either metric to metric or
English to metric conversions
Conversion Chart
5 Steps of Problem Solving
1.) Identify what you are asked.
2.) Write down what is given or known.
3.) Look for relationships between knowns
and unknowns (use charts, equations).
.4.) Rearrange the equation to solve for the
unknown.
5.) Do the computations, cancel the units,
check for reasonable answers.
Write the KNOWN, identify the
UNKNOWN.
• EX. How many quarts is 9.3 cups?
9.3 cups = ? quarts
Draw the dimensional “jumps”.
Cupspintsquarts
2 cups=1pint
2 pints= 1quart
2 cups=1pint
2 pints= 1quart
Cupspintsquarts
Insert relationship so units cancel.
9.3 cups
1
x
1 pint
2 cups
Do Math
x
1 quart
9.3 x 1 x = 9.3
2 pints
1x2x2= 4
Cancel units
Answer: 9.3 cups= 2.325 quarts
• EX. How many quarts is 9.3 cups?
Step 1. Identify what you are asked
9.3 cups =
Step 2. Write down what is given or known.
? quarts
Step 3. Look at relationships between known and unknown
Conversion Chart
Draw the dimensional “jumps”.
2 cups=1pint
2 pints= 1quart
Cups  pints  quarts
Step 4. Rearrange the equation to solve for the unknown.
9.3 cups
1
1 pint
2 cups
1
2
quart
pints
• EX. How many quarts is 9.3 cups?
5. Do the computations, cancel the units, check for reasonable answers.
9.3 cups
1
X
X
1 pint
2 cups
X
X
1 quart
2 pints
*Multiply all the numbers along the top
*Multiply all the numbers along the bottom
*Divide the two numbers
Answer: 9.3 cups= 2.325 quarts
=
9.3
4
Practice Problems
Conversion Chart
1.) 12 m=_____ in
Ans.: 12 m =
meters  feet  inches
12 m X 3.28 ft X 12 in
1
X
1m
X
472.32
=
1
1 ft
2.) 15.6 in=_____ ft
Inches  feet
15.6 in
1
X
1 ft
X
12 in
Ans.: 15.6 in =
15.6
=
1
X
1 Kg
12 inches=1 foot
12
3.) 0.0034 kg=_____ oz.
Kilograms  ounces
0.0034 kgX35.27 oz
1 meter= 3.28 feet
1 foot=12 inches
=
0.120
1
Ans.: 0.0034 kg =
1 Kilogram=35.27 oz
Dimensional Analysis Practice
1. 12.45 mi =____________ km
2. 1234 mL =____________ L
3. 0.567 cm =____________ in
4. 203 lbs. =____________ Kg
5. 3456.67 gal =__________ L
Individual Practice
1.) 12.45 mi =_______ yd
2.) 1 cup = _______ gal
3.) 0.567 cm =_______ km
Conversion Practice
1.) 1000 mg = _______ g
2.) 1 L = _______ mL
3.) 160 cm = _______ mm
4.) 14 km = _______ m