- WELCOME TO OUR VIDEO TUTORIAL ON SCIENTIFIC NOTATION.
NOW DEFINITELY, YOU WANT TO HAVE YOUR CALCULATOR
WITH YOU TO PRACTICE WHAT WE'RE WORKING ON.
SO, I'M GOING USE THE TI-30X IIS CALCULATOR.
SO, IF YOU DON'T HAVE THIS CALCULATOR THAT'S FINE.
IT'S JUST THAT YOUR KEY STROKES
AND THE BUTTON SEQUENCE MAYBE A LITTLE DIFFERENT.
SO, FOR SCIENTIFIC NOTATION BECAUSE IN CHEMISTRY
WE WORK WITH VERY SMALL NUMBERS AND VERY LARGE NUMBERS,
WE OFTEN WANT TO PUT THEM SO THEY'LL
BE SOME VALUE OF COEFFICIENT,
AND THEN THAT WILL BE MULTIPLIED BY THE EXPONENTIAL TERM.
SO, NOW THIS COEFFICIENT IT'S GOING TO BE A NUMBER BETWEEN
ONE AND TEN.
SO, THERE WILL ALWAYS BE ONE DIGIT TO THE LEFT OF THE DECIMAL
AND THEN THE NUMBER OF DIGITS
TO THE RIGHT WILL DEPEND ON THE SIG FIGS.
SO, IF YOU ARE UNSURE ON SIG FIGS
THERE IS A SEPARATE VIDEO TUTORIAL
THAT WILL REVIEW SIG FIGS FOR YOU TO HELP YOU.
AND THEN OF COURSE WE HAVE THE EXPONENTIAL TERM.
OKAY, SO EXPONENTS.
SO EXPONENTS ARE PREREQUISITE
OF CHEMISTRY CLASSES AND WORKING WITH THEM.
AND SO I'LL GIVE A VERY BRIEF REVIEW JUST TO JOG YOUR MEMORY
IF YOU NEED MORE YOU'RE GOING TO WANT TO SEEK HELP
AT THE MATH LAB OR SOMETIMES THE APPENDIX
IN YOUR TEXTBOOK WILL HAVE SOME EXTRA INFORMATION.
SO, REMEMBERING THAT WHEN WE HAVE A POSITIVE EXPONENT
WE CAN THINK OF THIS AS BEING A LARGE NUMBER.
SO, FOR EXAMPLE IF WE HAD 10 TO THIRD
THAT'S 10 X 10 X 10, RIGHT,
10 MULTIPLIED BY ITSELF THREE TIMES OR A THOUSAND.
WHEN THE EXPONENTIAL TERM IS A NEGATIVE NUMBER
OR LESS THAN ONE,
THEN WE ARE GOING TO HAVE VERY SMALL NUMBERS.
SO, FOR EXAMPLE IF WE HAVE 10
TO THE MINUS THREE WE CAN REWRITE THAT ONE OVER 10
TO THE THIRD WHICH IS ONE OVER 10 X 10 X 10.
WHICH IS ONE OVER A THOUSAND OR 0.001. ALL RIGHTY.
SO, NOW LET'S GET TO WORKING WITH NUMBERS
IN SCIENTIFIC NOTATION WITH OUR CALCULATORS.
SO, YOU WANT TO HAVE YOUR CALCULATOR OUT AND READY
BECAUSE IT'S REALLY IMPORTANT YOU WANT TO BE ABLE
TO TOGGLE BACK AND FORTH BETWEEN DECIMAL NOTATION
WHICH THAT THE CALCULATOR CALLS FLOW
AND THEN SCIENTIFIC NOTATION.
SOMETIMES WE'LL WANT TO WORK WITH NUMBERS
IN THEIR TRADITIONAL FORMAT
AND SOMETIMES IN SCIENTIFIC NOTATION.
SO, FOR THE HP CALCULATOR THAT I GAVE YOU THE MODEL FOR,
WHAT WE WANT TO DO IS, LET'S SAY I ENTER,
I DON'T KNOW, 35,000, OKAY.
SO, HERE'S THIS VALUE--
OOPS, CLEAR THAT UP.
LET'S SAY 35,000 ALL RIGHTY,
NOW IF I WANT THIS TO BE IN REGULAR FLOATING NOTATION
WE GO SECOND FUNCTION AND THEN WHEN IT SAYS SCI ENGINEERING,
I CAN TOGGLE TO FLOW AND I SAY YES,
THAT'S WHAT I WANT.
SO, NOW WE SEE THAT THE NUMBER IS DISPLAYED IN DECIMAL,
NORMAL FLOATING NOTATION,
LET'S SAY I WANT TO TOGGLE TO SCIENTIFIC.
WE GO BACK TO THE SECOND FUNCTION
AND THEN SCI ENGINEERING WE USE THE ARROW KEYS
TO GO OVER TO THE SCI MODE AND PRESS ENTER AND NOW NOTICE
THAT THE NUMBER IS WRITTEN IN SCIENTIFIC NOTATION.
THERE'S ONLY ONE THING THAT THE CALCULATOR CAN'T DO FOR YOU.
IT DOESN'T KNOW ABOUT SIG FIGS.
SO, REMEMBER WHEN WE'RE DOING SCIENTIFIC NOTATE--
OR SCIENTIFIC NOTATION,
RIGHT, THAT THE COEFFICIENT HAS THE SIG FIGS TIMES THE EXPONENT.
SO, THIS IS WHERE THE HUMAN STILL HAS TO COME INTO PLAY.
THE CALCULATOR WON'T BE ABLE TO HELP YOU THERE.
NOW, WE KNOW HOW TO TOGGLE BACK AND FORTH,
LET'S LOOK AT HOW WE COULD ACTUALLY ENTER A NUMBER
IN SCIENTIFIC NOTATION.
SO, I'LL CLEAR THE DISPLAY AND SO LET'S SAY WE WANTED TO ENTER
THE NUMBERS 6.02 X 10 TO THE 23RD,
RIGHT, SO WE ENTER OUR COEFFICIENT 6.02
AND NOW IT'S VERY IMPORTANT FOR CALCULATIONS,
WE WANT TO LINK THIS ALL TOGETHER.
THIS IS ONE NUMBER,
THIS IS ONE MEASUREMENT, ONE VALUE.
SO, IT'S IMPORTANT THAT WE LINK THEM.
SO, THE WAY WE CAN DO THAT IN OUR CALCULATOR IS WE CAN
TAKE ADVANTAGE OF THE ENTER EXPONENT BUTTON THERE EE.
SO, ONCE AGAIN WE NEED THE SECOND FUNCTION,
WE'RE GOING TO ENTER THE EXPONENT
AND THEN THE EXPONENT IS 23.
SO, THEN WE CAN SEE HERE IS THE VALUE
IN SCIENTIFIC NOTATION.
SO, LET ME DRAW SOMETHING--
I'M GOING TO SLIDE THIS OVER TO THE OTHER SIDE, ALL RIGHT.
SO, IF WE USE THE SECOND FUNCTION
AND THEN THE BUTTON SAYS X
- 1 BUT IT HAS EE ON THE TOP
AND SO WHEN WE PUSH THESE TWO KEYS TOGETHER,
THAT GIVES US THE TIMES AND THE 10.
SO, THE PART THAT WE ENTER,
IS WE ENTER THE COEFFICIENT AND WE ENTER THE EXPONENT
AND THEN THE TIMES 10 IS THROUGH THE SECOND FUNCTION EE KEY.
AND THIS IS VERY IMPORTANT
BECAUSE IT'S GOING TO HELP YOU AVOID CALCULATION ERRORS.
IF YOU USE A DIFFERENT SET
OF KEY STROKES AND YOU FIND THAT YOU'RE ALWAYS OFF
BY A FACTOR OF 10 ON YOUR CALCULATIONS
OR YOUR FINAL RESULT HAS THE OPPOSITE SIGN FOR THE EXPONENT,
THEN IT MEANS THAT YOU'RE HAVING A CALC ERROR
BECAUSE YOU'RE NOT USING YOUR CALCULATOR
THE WAY IT WAS ENGINEERED.
ALL RIGHTY.
SO, NOW LET'S PRACTICE THIS.
SO, LET'S CONVERT THE FOLLOWING NUMBERS FROM DECIMAL
TO SCIENTIFIC NOTATION OR VICE VERSA.
SO, WE'LL CLEAR OUT THE CALCULATOR,
3.5, ENTER EXPONENT.
NOW, FOR THE NEGATIVE HERE THIS MINUS THREE,
WE WANT TO USE THE MINUS BUTTON HERE,
MINUS THREE ENTER. OKAY.
SO, IT'S STILL IN SCIENTIFIC NOTATION,
SHARE THE BEST VISIBILITY,
LET'S TRY IT OVER THERE. OKAY.
SO NOW WE WANT TO PRACTICE TOGGLING BACK AND FORTH.
SECOND FUNCTION, SCI ENGINEERING,
LET'S PUT IT INTO FLOATING THERE WE GO SO,
.0035. NOW COMES THE PART WHERE THE CALCULATOR
CAN'T HELP US WITH SIG FIGS.
NOTICE IN THIS NUMBER HOW MANY SIG FIGS ARE THERE,
THERE ARE FOUR.
SO, WHEN WE WRITE IT IN DECIMAL OR FLOATING NOTATION,
REMEMBER LEADING ZEROS NEVER COUNT.
SO, WE WOULD NEED TO ADD THESE TWO TRAILING ZEROS
SO THAT WE PRESERVE THE SIG FIGS OF THE VALUE.
ALL RIGHTY.
SO NOW LET'S PRACTICE THE NEXT ONE.
TWO HUNDRED AND THIRTY EIGHT THOUSAND, YOU ENTER IT.
WE'RE IN FLOW OR DECIMAL MODE,
WE'LL GO BACK AND TOGGLE TO SCIENTIFIC NOTATION
AND NOW WE HAVE THE VALUE IN SCIENTIFIC NOTATION 10 TO FIFTH.
ALL RIGHT.
SO, NOW WE CAN PRACTICE ENTERING ANOTHER NUMBER
WITH OUR EXPONENT,
OR ENTERING EXPONENT KEY
2.021 SECOND FUNCTION ENTER THE EXPONENT FIVE.
OH, OKAY.
WE'VE ENTERED IT BUT IT STILL
IN SCIENTIFIC NOTATION SECOND FUNCTION,
GO BACK TO FLOW AND NOW WE HAVE IT IN DECIMAL
OR FLOATING NOTATION AND WE'LL MAKE SURE RIGHT,
WE WONT TO PUT THE DECIMAL POINT
BECAUSE WE WANT TO MAINTAIN THE SIG FIGS.
SO, IF WE'RE CONVERTING BETWEEN FLOATING MODE OR DECIMAL MODE
IN SCIENTIFIC NOTATION THAT NEVER CHANGES THE SIG FIGS.
THEY SHOULD ALWAYS BE THE SAME.
AND NOW FOR THIS LAST ONE, .000167,
WE ENTER THAT, WE WANT TO CHANGE IT TO SCIENTIFIC NOTATION
SECOND FUNCTION SCI AND ENTER,
THERE WE GO AND BOTH RESULTS--
BOTH VALUES ARE THREE SIG FIGS.
ALL RIGHTY.
SO, THESE ARE SOME IMPORTANT BUTTONS
THAT YOU WANT TO GET COMFORTABLE USING SWITCHING BACK AND FORTH
AND BEING ABLE TO ENTER NUMBERS IN SCIENTIFIC NOTATION.
AND NOW LET'S PRACTICE DOING SOME CALCULATIONS.
ALL RIGHTY.
SO, WE'LL JUST USE SOME GENERIC SCIENTIFIC NOTATION TERMS.
SO, IF WE HAVE A
TO THE 10 X 10 TO THE X MULTIPLIED BY B X 10
TO THE Y. WHEN WE'RE MULTIPLYING TERMS
IN SCIENTIFIC NOTATION WE MULTIPLY THE COEFFICIENTS
AND THEN WE ADD THE EXPONENTIAL TERMS.
AND THEN IN A SIMILAR WAY,
IF WE ARE USING DIVISION,
WE DIVIDE THE EXPONENTS--
EXCUSE ME, WE DIVIDE THE COEFFICIENTS
AND WE SUBTRACT THE EXPONENTS.
SO, I WANT YOU TO USE YOUR CALCULATORS
AND BE COMFORTABLE USING YOUR CALCULATORS
BUT IT CAN BE VERY HELPFUL TO BE ABLE TO DO AN--
A BALLPARK CALCULATION IN YOUR MIND SO,
YOU CAN RECOGNIZE IF YOU HAVE A CALC ERROR BECAUSE MANY TIMES
I SEE THAT STUDENTS HAVE A CORRECT SETUP
BUT THEY HAVE A CALCULATION ERROR PROBLEM.
SO, THERE'S ONE LAST THING TO BE AWARE
OF IS THAT OUR CALCULATORS ARE PROGRAMMED TO FOLLOW THE ORDER
OF OPERATIONS.
SO, THE ORDER OF OPERATIONS IS PEMDAS.
SO, REMEMBER THAT ANYTHING IN PARENTHESIS
WILL BE PERFORMED FIRST AND THEN THE EXPONENTS,
THEN MULTIPLICATION AND DIVISION
AND LAST BUT NOT THE LEAST ADDITION AND SUBTRACTION.
AND SO THIS IS WHY THE ORDER
OF OPERATIONS IS WHY IT'S SO IMPORTANT
TO USE YOUR EXPONENT KEY
WHEN YOU'RE ENTERING NUMBERS AND SCIENTIFIC NOTATION
BECAUSE OTHERWISE THE ORDER OF OPERATIONS
CAN CREATE A CALC ERROR EVEN IF YOU HAVE THE CORRECT SETUP.
SO, I'D LIKE TO DO A QUICK TEST RIGHT NOW
TO SEE HOW COMFORTABLE YOU ARE WITH YOUR CALCULATOR.
SO, I'M GOING TO WRITE A VERY SIMPLE, RIGHT?
25 DIVIDED BY 5 X 5. NOW, I KNOW
WE CAN ALL DO THIS IN OUR HEAD VERY SIMPLY AND GET THE ANSWER.
BUT I WANT TO--
THIS IS A QUICK TEST OF YOUR CALCULATION SKILLS.
SO, GO AHEAD AND ENTER THIS CALCULATION
INTO YOUR CALCULATOR THE WAY
YOU NORMALLY WOULD AND SEE WHAT RESULT YOU GET.
IDEALLY, YOU SHOULD BE GETTING A VALUE OF ONE
BECAUSE THIS ISN'T--
THIS IS 25 DIVIDED BY 25 WHICH IS ONE.
HOWEVER IT'S POSSIBLE
THAT SOME OF YOU MAY HAVE GOT THE WRONG ANSWER.
IF YOU GOT AN ANSWER OF 25 WHICH IS WRONG THEN
YOU HAVE JUST BEEN BIT BY THE PEMDAS BUG.
SO, WHEN WE'RE DOING CALCULATIONS,
IT'S IMPORTANT TO RECOGNIZE ALL TERMS
IN THE DENOMINATOR ARE DIVIDED.
ALL TERMS IN THE NUMERATOR ARE MULTIPLIED.
SO, THE KEYSTROKES
TO GET THE CORRECT ANSWER ARE 25 DIVIDED BY FIVE.
AND THEN AT THIS POINT I ENCOURAGE YOU TO PUT AN EQUALS
OR AN ENTER TO PERFORM THIS CALCULATION.
AND THEN THE SECOND FIVE--
IT'S TRUE, THESE ARE MULTIPLIED TOGETHER
BUT THEY'RE IN THE DENOMINATOR.
SO, FOR THE OVERALL EXPRESSION THEY NEED TO BE DIVIDED.
DIVIDED BY FIVE, WHICH GIVES US THE CORRECT ANSWER OF ONE.
SOME OF YOU MAY BE WONDERING, "WHAT DID I DO WRONG HERE,
HOW DID I GET 25?" WELL,
IF WE DID 25 DIVIDED BY FIVE
BUT THEN WE MULTIPLY BY FIVE IS--
YOU COULD SEE THE PROBLEM HERE, RIGHT?
25 DIVIDED BY 5 IS 5 X 5 GETS US THE WRONG ANSWER.
SO, THERE ARE SEVERAL WAYS
TO FIX THIS IF YOUR CALCULATOR HAS PARENTHESIS MAKE SURE
TO PUT PARENTHESIS AROUND YOUR DENOMINATOR TERMS USING EQUALS
TO EXECUTE SO THAT WE DON'T BUILD UP ON OUR ORDER
OF OPERATIONS AND JUST KEEPING IN MIND THAT ALL TERMS
IN THE DENOMINATOR ARE DIVIDED.
ALL RIGHTY.
SO, NOW, WE GOT--
WE HAVE A COUPLE PRACTICE PROBLEMS
HERE FOR YOU TO BUILD CONFIDENCE
AND BEING COMFORTABLE WITH YOUR CALCULATOR.
SO, GO AHEAD IF YOU WANT AND PAUSE THE VIDEO FOR A MINUTE
AND DO THE CALCULATIONS AND THEN WE CAN COMPARE ANSWERS.
SO, AND ALL--
FOR THE VIDEO, I'LL JUST GO AHEAD
AND DO THE KEYSTROKES ON HERE TO HELP YOU BUILD YOUR SKILLS.
SO, LET'S PUT THAT THERE I THINK.
ALL RIGHTY.
SO, WE WOULD ENTER THE FIRST NUMBER 2.34--
WE DON'T HAVE TO WORRY ABOUT THE ZERO.
ENTER EXPONENT MINUS THREE,
MULTIPLY 2.6, ENTER EXPONENT SIX EQUALS.
AND SO NOW WE GET THE RESULT, 6.084 X 10 TO THE THIRD
AND THE LAST THING IS THE CALCULATOR
CAN'T HELP US WITH SIG FIGS,
I'M GOING TO SLIDE THIS OUT OF THE WAY.
SO, LAST BUT NOT THE LEAST THEN WE LOOK AT,
WILL CAN I CONSIDER THESE NUMBERS AS MEASUREMENTS
AND SO WE HAVE FOUR SIG FIGS AND TWO SIG FIGS
SO OUR FINAL RESULT SHOULD BE TWO SIG FIGS SO,
WE WOULD REPORT 6.1 TIMES TEN TO THE THIRD.
OKAY. NOW, THIS ONE--
BECAUSE EVERYTHING WAS IN THE NUMERATOR,
YOU CAN USE BAD TECHNIQUE AND STILL GET THE CORRECT ANSWER.
SO, LET'S TRY A MORE CHALLENGING CALCULATION,
LIKE, THE ONE BELOW.
ALL RIGHTY.
SO, HERE'S OUR NUMERATOR TERM,
3.506, ENTER THE EXPONENT THREE.
NOW, WE'RE GOING INTO THE DENOMINATOR SO,
EVERYTHING IN THE DENOMINATOR GETS DIVIDED.
DIVIDED BY 5.7 ENTER EXPONENT SEVEN
AND I'M JUST GOING TO GO AHEAD AND EXECUTE THAT SO,
THAT I DON'T WORRY ABOUT PEMDAS.
AND NOW, I'M GOING TO--
WE'RE GOING TO DIVIDE AGAIN
BECAUSE THIS TERM IS ALSO IN THE DENOMINATOR.
DIVIDED BY 2.61 ENTER EXPONENT MINUS TWO EQUALS.
ALL RIGHTY.
SO, WE GET THE--
OUR CALCULATOR SPITS OUT A NICE BIG NUMBER FOR US.
7 X 10 TO THE
-3, SLIDE THIS OUT OF THE WAY.
NOW, LAST BUT NOT THE LEAST, LET'S LOOK AT SIG FIGS.
SO, THIS TOP VALUE WAS FOUR, TWO,
AND THREE SIG FIGS.
SO, THE WORST DATA LIMITS OUR RESULT SO,
WE WOULD REPORT THIS AS 2.4 TIMES TEN
TO THE MINUS THREE. OKAY.
AND LET'S DO ONE MORE PRACTICE TO MAKE SURE
THAT EVERYONE IS GOING TO GET ALL OF THE POINTS THEY SHOULD.
AND ALWAYS A SAD TO SEE A PERFECT SETUP
WITH A CALC ERROR.
SO, LET'S GET RID OF THOSE.
ALL RIGHTY.
7.4 ENTER THE EXPONENT--
OOPS, I DON'T KNOW WHY I DID THAT.
MINUS TWO EVERY TERM IN THE DENOMINATOR IS DIVIDED.
3.248 EXPONENT SIX,
WE'LL GO AHEAD AND EXECUTE THAT ENTRY.
AND THEN WE HAVE ANOTHER TERM IN THE DENOMINATOR SO,
IT ALSO IS DIVIDED.
ENTER EXPONENT MINUS THREE EQUALS, HENCE, THEN,
WE COULD GET THE VALUE 3.505 TIMES TEN TO THE MINUS SIX.
SO, NOW, WE CAN CHECK FOR OUR SIG FIGS,
TWO SIG FIGS UP HERE,
FOUR, AND THREE SO, OUR FINAL RESULT
WILL BE REPORTED TO TWO SIGNIFICANT FIGURES.
AND SO THAT WOULD BE 3.5 TIMES TEN TO THE MINUS SIX.
ALL RIGHTY.
SO, THAT CONCLUDES THE OVERVIEW AND--
OF SCIENTIFIC NOTATION WITH PRACTICE USING OUR CALCULATOR
IN PERFORMING CALCULATIONS.
SO, GO AHEAD AND TAKE SOME TIME NOW
TO WORK A FEW PRACTICE PROBLEMS TO REINFORCE YOUR UNDERSTANDING.