Dimensional Analysis
Metric System
Let’s look at the chart again.
Let’s look at the chart again.
Meter, Liter, GramStandard Unit SI
Let’s look at the chart again.
Kilo
Kilo comes the Greek word meaning “thousand”
So we use this word and prefix to indicate that there are a thousand of the SI unit in one Kilo
EXAMPLE: 1000m = 1 km1000 L = 1 kL1000g = 1kg
Let’s look at the chart again.
Centi
• Centi comes the latin word meaning “hundred”
• Think of a Penny. One hundred pennies makes a dollar.
• 100 years makes a century• In dimensional analysis, a centi is SMALLER
than the SI unit.
Centi
• 100 cm = 1m• 100 cg = 1 g• 100 cL = 1 L
Let’s look at the chart again.
milli
• Latin word for “thousand”• Millipede (one thousand, pedis means foot)• A milli is smaller than the SI unit
• 1000 mL = 1L• 1000 mg = 1g• 1000 mm = 1m
• EX. How many meter are in 925 km?
925 km ? m=
Draw the dimensional “jumps”.
925 km ? m=
925 km x
* Use charts or tables to find relationships
Insert relationship so units cancel.
925 km xkm
*units of known in denominator (bottom) first*** units of unknowns in numerator (top
m
1
1,000
Cancel units
925 km xkm
m
1
1,000
Do the Math
925 km xkm
m
1
1,000
1 x 1=
925 x 1,000
1=
925,000= 925,000
How wide is our universe?
210,000,000,000,000,000,000,000 miles(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in
scientific notation.
Scientific Notation
A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where would you put the decimal to make this number be between 1 and
10?
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
23
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
23When the original number is more than 1,
the exponent is positive.The answer in scientific notation is
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
23When the original number is more than 1,
the exponent is positive.The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many places?
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many places?
8
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many places?
8When the original number is less than 1, the
exponent is negative.
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many places?
8When the original number is less than 1, the
exponent is negative.9.02 x 10-8
LecturePLUS Timberlake 31
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x ?? 1 day
LecturePLUS Timberlake 32
Solution
Unit plan: days hr min seconds
1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min
= 1.2 x 105 sec
Accuracy versus Precision
• Accuracy: how close you are to the actual value
• Precision: the ability to measure with exactness, repeatability.
Accuracy versus Precision
• VALUES IN DATA: • 12.33 cm• 12.21 cm• 12.27 cm• 12.24 cm
• ACTUAL VALUE: 99 cm
The data is precise, but not accurate
Accuracy versus Precision
• VALUES IN DATA:• 95.89 cm• 101.22 cm• 96.80 cm• 99.2 cm
• ACTUAL VALUE: 99 cm
The data is accurate but not precise
Accuracy versus Precision
• VALUES OF DATA:• 14.53 cm• 99.49 cm• 57.90 cm• 32.84 cm
• ACTUAL VALUE: 99 cm
The data neither accurate nor precise
Accuracy versus Precision
• VALUES OF DATA:• 99.87 cm• 99.12 cm• 98.99 cm• 99.53 cm
• ACTUAL VALUE: 99 cm
The data is both accurate and precise.
CALCULATING DEGREE OF ERROR
• Measurement – Actual Value X 100 Actual Value
EX: measurement is 29. Actual Value is 27.5
29 – 27.5 X 100 = 5.45% percentage of error 27.5
OTHER MEASUREMENTS
• VOLUME = L , cm3, cc• MASS= g• LENGTH= m• DENSITY = g/ml, g/cm3
LET’S REVIEW
The student determines that the unknown substance is sodium chloride. Which of the following is an extensive property of sodium chloride?•Mass of 15 g•White color•Density of 2.17 g/cm3
• Solubility in water19.
The safest way to dilute concentrated sulfuric acid is to add:
– A series of small volumes of water to the acid while stirring.
– The acid to water slowly while stirring constantly.– The acid to a small volume of water and then add
more water.– Dilute sulfuric acid to a small volume of the
concentrated acid.
• WHAT HAPPENED TO THE DENSITY OF THE SUBSTANCE???
What is the most appropriate unit of measure for reporting the density of a solid?
– g/cm3
– g/cm– g/L2
– g/mm2
Volume is space the matter takes up
cm3 = cc = mL
• These are the measurements of volume.
• The METRIC measurement for VOLUME is mL
• There will be at least three questions when you will need to know this.
Jeremy decides to cook some pasta noodles. He notices that the directions say to add salt to water before bringing it to a
boil. The next day, Jeremy asks his science teacher, Ms. Jackson, a question: “How does adding salt affect the way water boils?” Ms. Jackson then asks Jeremy to plan and
conduct an experiment to find the answer. The following graph summarizes Jeremy’s results. Which list of materials
and equipment best represents what Jeremy would have used in order to get these results?
• Beaker, water, pasta, table salt, pipette, hot plate, measuring spoon.
• Beaker, water, pasta, table salt, pH meter, hot plate, spatula, ring stand.
• Beaker, water, pasta, table salt, thermometer, hot plate, timer, ice cubes.
• Beaker, water, pasta, table salt, thermometer, hot plate, spatula, balance.
Which of the following pieces of equipment would be most appropriate for measuring the volume of a marble?
How many significant figures
• 32.983• 8.000• 4839.4• 0.000000000000023• 23,000.0• 450,057
What do these PREFIXES mean
• Kilo• Centi• Milli
KILO
• Greek for ‘thousand’• Means 1000 times larger
Centi
• Latin for ‘hundred’• Mean 100 times SMALLER
milli
• Latin for ‘thousand’• Means 1000 times smaller
Temperature Conversions
Ko= Co + 273 Co = Ko - 273Fo = 9/5 (Co +32) Co = 5/9 (Fo-32)
WHAT YOU’RE GIVEN ON THE STAAR EXAM AND TAKS
0 Co = 273 Ko
Precision and Accuracy
Team 1- 2.65 cm Team 2 - 2.75 cm Team 3 - 2.80 cmTeam 4 - 2.77 cm ACTUAL MEASUREMENTTeam 5 - 2.77 cm 2.70 cm Team 6 - 2.65 cm
Accurate, precise, both or neither
Percentage of Error
• Measurement – actual value X 100 = %
actual measurement
EXAMPLE: team 1 2.65
2.65 – 2.70 X 100 = 1.85 % 2.70
The quantitative measurement among the following is:
– The oak tree is taller than the maple.– The oak tree is very tall.– The oak tree is 15 meters tall.– The oak tree is taller than the house.
•
Study Well
• Belief is half the battle. Good Luck
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