math and scientific method unit 1. chemistry math topics scientific notation significant figures...
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Math and Scientific Method
Unit 1
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Chemistry Math Topics Scientific Notation Significant Figures (sigfig) Rounding Exponential Notation SI System Metric Conversion Factor Labeling Density Percent Error
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Significant Figures
When a scientist measures something the precision of the investigator and instruments must be considered
ALL digits that are part of the measurement are significant (important) but sometimes numbers are used as place holders and not significant
These are usually zeros
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Sigfig Rules
Zero’s between digits are significant 700007 has 6 sigfig
Zero’s after digits when no digit is present are not significant 120000 has only 2 sigfig
Decimals change the rules
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Decimal Rules
If a decimal is present Zeros to the right of the decimal are
significant 12.00 has 4 sigfig
Zeros to the left of the decimal are significant 3400. is significant
Zeros to the left of the digits BUT the right of the decimal are NOT significant 0.00234 has only 3 sigfig
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Rounding
Basic rules from math “5 and above, give it a shove; four
and below, just let it go.” DJ Because you must round to sigfig, you
may need to look at several digits to round
DO NOT ROUND UNTIL THE FINAL ANSWER!
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Rounding to Sigfig
For addition and Subtraction- the last digit to the right in the answer must be the same as the LEAST precise in the problem-24.5 +6.2718.23 BUT the sigfig is 18.2
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For multiplication and division the answer must have the same number of digits as the least precise in the problem
48.4398X1.5273.628496 but in sigfig it is 73.6
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Exponential Notation
A way to express numbers that are very large or very small
Here are the rules Only use sigfig Decimal always goes after the 1st digit The exponent represents the number of
spaces moved by the decimal Positive number if it moves to the left Negative if it moves to the right
120 000 000 = 1.2x108
0.000 003 450 = 3.450 x10-6
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SI units – Le System International d’Unites
Measurement represents quantity Something that has magnitude, size or
amount The single measurement system that
all scientists have agreed to They are of constant value Standardization in style and format
were also determined
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SI Base Units
Length – meter Mass - kilogram Time - Second Temperature – Kelvin Amount of substance - mole Electric Current - ampere Luminous intensity - Candela
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SI Prefixes
Prefixes added to the names are used to represent quantities that are larger or smaller than the base units
You are expected to know these K,h,da,unit,d,c,m And recognize the rest
Know the exponential notation for each
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Metric conversion
Moving from one SI unit to another is metric conversion
Moving the decimal point is how it works
Practice is the only way to learn this skill
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Factor Labeling
Used to help change the UNITS of something, so that numbers are still equivalent
Math Fact: Multiplying by one does not change the value of a number
When the numerator and denominator are equivalent (equal) then it is like multiplying by one
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If you have 12 dozen donuts, how many donuts do you have? See you can use factor labeling (12 dozen) x 12 donuts = 144 donuts
1 dozen
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Here are the steps
Identify what you have and what you need I have 2.5 miles and I need to know how
many feet Put a one in front of the unit you
have, and how many of the other unit is equal to (look it up) 1 mile=5280 feet
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Set up the problem 2.5 mile x 5280feet
1 mile Solve Put it into sigfig
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Practice Practice Practice
A car is traveling 65 miles per hour. How many feet des it travel in one second?
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Convert the following 7.02 kg to lbs 8 L to quarts 15 inches to cm 98 kg to slugs 45 kcal to J
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Now they will get harder
If a man can move 35 lbs of dirt per minute, how many kg per hour will he move?
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More two unit problems
78 miles/hour to meters/sec .345 mm/sec to inches per minute 476 gallons/ hour to pints per minute
You’ll see more…
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Percent Error
How far away from the accepted value are you?
Theoretical = actual (Actual value – expected value) x100 =
actual value Percent error
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Practice
Actual 45.6 Expected 46.0 89.4 95.0
1238.369 1225.
You get the drift….
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Accuracy and Precision
Accuracy – how close you answer is to the accepted value The closer you are to the correct answer,
the more accurate you are Precision
How similar your range of answers are You want to be both right ( accurate)
and repeatable (precise)
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Scientific Method
A quick review A process used to test a hypethosis Hypothesis is a tentative explanation to
a problem or question that is based on observation or past knowledge
A hypothesis must be tested through valid experimentation
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Steps in Scientific Method Formulate a hypothesis Test the hypothesis
Using controlled experiments with experimental and dependent variables Experimental – what you change Dependent – what changes as a result
Obtain data, document and analyze it Draw conclusion Publish for peer review