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

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

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

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

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!

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

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

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

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

SI Base Units

Length – meter Mass - kilogram Time - Second Temperature – Kelvin Amount of substance - mole Electric Current - ampere Luminous intensity - Candela

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

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

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

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

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

Set up the problem 2.5 mile x 5280feet

1 mile Solve Put it into sigfig

Practice Practice Practice

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

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

Now they will get harder

If a man can move 35 lbs of dirt per minute, how many kg per hour will he move?

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…

Percent Error

How far away from the accepted value are you?

Theoretical = actual (Actual value – expected value) x100 =

actual value Percent error

Practice

Actual 45.6 Expected 46.0 89.4 95.0

1238.369 1225.

You get the drift….

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)

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

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