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Math and Scientific Method

Math and Scientific Method. Unit 1. Chemistry Math Topics. Scientific Notation Significant Figures (sigfig) Rounding Exponential Notation SI System Metric Conversion Factor Labeling Density Percent Error. Significant Figures.

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Math and Scientific Method

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  1. Math and Scientific Method Unit 1

  2. Chemistry Math Topics • Scientific Notation • Significant Figures (sigfig) • Rounding • Exponential Notation • SI System • Metric Conversion • Factor Labeling • Density • Percent Error

  3. 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

  4. 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

  5. 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

  6. 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!

  7. Rounding to Sigfig • For addition and Subtraction- the last digit to the right of the decimal in the answer must be the same as the LEAST precise in the problem -24.5 +6.27 18.23 BUT the sigfig is 18.2

  8. For multiplication and division the answer must have the same number of digits as the least precise in the problem 48.4398 X1.52 73.628496 but in sigfig it is 73.6

  9. 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

  10. 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

  11. SI Base Units • Length – meter • Mass - kilogram • Time - Second • Temperature – Kelvin • Amount of substance - mole • Electric Current - ampere • Luminous intensity - Candela

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. How to solve a problem • List the known variables • Set up the problem • 2.5 mile x 5280feet 1 mile • Solve • Put it into sigfig

  18. Practice Practice Practice • A car is traveling 65 miles per hour. How many feet des it travel in one second?

  19. Convert the following • 7.02 kg to lbs • 8 L to quarts • 15 inches to cm • 98 kg to slugs • 45 kcal to J

  20. Now they will get harder • If a man can move 35 lbs of dirt per minute, how many kg per hour will he move?

  21. 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…

  22. Percent Error • How far away from the accepted value are you? • Theoretical = actual • (Actual value – expected value) x100 = actual value • Percent error

  23. Practice • Actual 45.6 Expected 46.0 89.4 95.0 1238.369 1225. You get the drift….

  24. 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)

  25. 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

  26. 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

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