- WELCOME TO AN INTRODUCTION TO PERCENTS.
THE MAIN GOAL OF THIS VIDEO IS TO CONVERT BETWEEN PERCENTAGES,
DECIMALS AND FRACTIONS.
IN MATHEMATICS A PERCENTAGE IS A WAY OF EXPRESSING A NUMBER
AS A FRACTION OF 100,
PERCENT MEANING PER HUNDRED.
IT IS OFTEN DENOTED WITH A PERCENT SIGN AS WE SEE HERE.
IF THERE IS A 10% CHANCE OF RAIN TOMORROW
THAT MEANS THERE ARE 10 CHANCES OUT OF 100.
SO 10% = 10/100 OR TEN-HUNDREDTHS,
WHICH CAN BE SIMPLIFIED TO 1/10,
WHICH CAN ALSO BE WRITTEN AS A DECIMAL IN THE FORM OF 0.1.
HERE ARE SOME INTERESTING STATISTICS INVOLVING PERCENTAGES
IN THE UNITED STATES.
THE TOP 20% OF THE POPULATION
OWNS OVER 80% OF ALL OF THE WEALTH IN THE U.S.
THE TOP 5% HAD MORE WEALTH
THAN THE REMAINING 95% OF THE POPULATION COLLECTIVELY.
AND THESE STATISTICS WERE FROM THIS WEBSITE.
AND I JUST FOUND A FEW OTHERS.
AMERICANS THROW AWAY 27% OF THE 350 MILLION POUNDS OF FOOD
THEY BUY EACH YEAR.
47% OF DOGS IN THE U.S. SLEEP IN A FAMILY MEMBER'S BED.
AND 76% OF AMERICAN COMMUTERS DRIVE TO WORK ALONE.
SO AS YOU CAN SEE, WE HEAR ABOUT PERCENTAGES EVERY DAY
WHEN WE TURN ON THE TV OR THE RADIO.
SO IT IS IMPORTANT THAT WE DO UNDERSTAND
WHAT PERCENTAGES MEAN.
LET'S GO AND TAKE A LOOK AT HOW WE'RE GOING TO CONVERT
BETWEEN PERCENTAGES, DECIMALS, AND FRACTIONS.
TO CONVERT FROM A PERCENT TO A FRACTION
WE WRITE THE NUMBER OF THE PERCENT OVER 100
AND THEN SIMPLIFY.
SO, FOR EXAMPLE, IF WE HAVE 15%
IN FRACTION FORM THAT WOULD BE 15/100.
NOTICE HOW WE DROP THE PERCENT SIGN.
AND THIS DOES SIMPLIFY.
THERE'S A COMMON FACTOR OF FIVE.
THIS IS EQUAL TO 3/20.
SO IT IS IMPORTANT THAT WE CONVERT OUR PERCENTAGES
TO FRACTIONS THAT WE ALSO SIMPLIFY.
NEXT, TO CONVERT A PERCENT TO A DECIMAL
WE DROP THE PERCENT SIGN AND THEN EITHER MULTIPLY BY 0.01
OR DIVIDE BY 100,
THE AFFECT IS THE SAME.
THE SHORTCUT IS TO DROP THE PERCENT SIGN
AND MOVE THE DECIMAL TO THE LEFT TWO PLACES.
SO, FOR EXAMPLE, IF I HAVE 8.3% IN DECIMAL FORM
I'LL DROP THE PERCENT SIGN,
MOVE THE DECIMAL TO THE LEFT TWICE, ONE, TWO,
AND THAT WOULD PRODUCE THE DECIMAL 0.083.
AGAIN, THE DECIMAL STARTED HERE,
WE MOVED IT LEFT TWICE OR DIVIDED BY 100,
AND THEN WE DROP THE PERCENT SIGN.
NOW, TO CONVERT FROM A DECIMAL TO A PERCENT
WE PRETTY MUCH DO THE OPPOSITE.
WE MULTIPLY BY 100 AND THEN ADD THE PERCENT SIGN.
SO IF WE HAVE THE DECIMAL 0.832, WE WOULD MULTIPLY THIS BY 100
WHICH IS EQUIVALENT TO MOVING THE DECIMAL PLACE TO THE RIGHT
TWICE THAT WOULD PRODUCE 83.2,
AND THEN WE ADD THE PERCENT SIGN.
SO WE SHOULD MAKE A NOTE HERE
THAT MOVING THE DECIMAL TO THE RIGHT TWICE
IS EQUIVALENT TO MULTIPLYING BY 100,
AND THAT WOULD BE THE SHORTCUT.
NEXT, WE'LL CONVERT A DECIMAL TO A FRACTION.
SO LET'S SAY WE HAVE THE DECIMAL 0.002.
THERE'S TWO WAYS TO DO THIS.
MY FAVORITE WAY IS JUST TO READ THE DECIMAL USING PLACE VALUE.
SO, FOR EXAMPLE, IF I WAS TO READ THIS
HERE ARE THE TENTHS, HUNDREDTHS, THOUSANDTHS,
I WOULD READ THIS AS TWO-THOUSANDTHS,
WHICH SIMPLIFIES TO 1/500.
NOW, IF YOU DON'T KNOW YOUR PLACE VALUES,
WHAT YOU CAN DO IS WRITE AS A FRACTION
WITH THE DENOMINATOR OF 1,
THEN MULTIPLY THE NUMERATOR AND DENOMINATOR BY POWERS OF 10
TO ELIMINATE ANY DECIMALS AND THEN SIMPLIFY.
SO LOOKING AT THAT THIS WAY
WE WOULD WRITE THE DECIMAL OVER ONE.
NOW WE'RE TIMING MULTIPLIED BY A POWER OF 10
WE MOVE THE DECIMAL OVER TO THE RIGHT ONCE.
SO WE HAVE TO MULTIPLY BOTH THE TOP AND THE BOTTOM
BY 10 TO THE 3RD
WHICH WOULD GIVE US 2/1000 WHICH IS EQUAL TO 1/500.
AGAIN, I THINK THE EASIEST WAY IS JUST TO READ THE DECIMAL
AS YOU WOULD USING PLACE VALUE.
OKAY. IN THE LAST TWO WE WANT TO CONVERT A FRACTION TO A DECIMAL.
SO, FOR EXAMPLE, IF WE HAVE THE FRACTION 2/5,
REMEMBER A FRACTION BAR IS A DIVISION SYMBOL.
THIS IS THE SAME AS 2 DIVIDED BY 5 WHICH WOULD EQUAL 0.4 OR 4/10.
AND LAST, WE NEED TO CONVERT A FRACTION TO A PERCENT.
THIS IS JUST A COMBINATION OF TWO PREVIOUS CONVERSIONS.
SO IF WE HAVE THE FRACTION 7/8
WE FIRST CONVERT IT TO A DECIMAL BY DIVIDING.
AND THEN WE MULTIPLY BY 100 AND ADD THE PERCENT SIGN.
REMEMBER THAT MULTIPLYING BY 100
WOULD BE THE SAME AS MOVING THE DECIMAL TO THE RIGHT TWICE
WHICH WOULD GIVE US 87.5%.
LET'S GO AND TAKE A LOOK AT COUPLE MORE EXAMPLES.
LET'S TAKE THE DECIMAL 1.2
AND CONVERT IT TO A PERCENT AND A FRACTION.
SO TO CONVERT TO A PERCENTAGE WE MULTIPLY BY 100,
ADD A PERCENT SIGN.
SO WE MULTIPLY BY 100, MOVE IT ONCE TO THE RIGHT THAT'S 12,
ONE MORE WOULD BE 120.
SO THIS WOULD BE 120%.
NOW TO FIND THE FRACTION NOTATION WE CAN USE EITHER ONE.
I LIKE GOING FROM PERCENT TO FRACTION
BECAUSE WE KNOW THAT A PERCENT IS A NUMBER COMPARED TO 100.
SO THIS IS 120/100.
NOW, THIS DOES SIMPLIFY.
WE CAN EASILY SEE THERE'S A COMMON FACTOR OF 10
WHICH WOULD GIVE US 12/10, WHICH SIMPLIFIES AGAIN TO 6/5.
NEXT WE HAVE A PERCENTAGE THAT WE WANT TO CONVERT TO A DECIMAL.
ON THIS PREVIOUS EXAMPLE WE MULTIPLIED BY 100
TO GET TO THIS.
SO TO GO FROM PERCENT TO DECIMAL WE DIVIDE BY 100.
SO WE'D MOVE THE DECIMAL TO THE LEFT TWICE,
WHICH WOULD GIVE US 0.0015 WITHOUT THE PERCENT SIGN.
AND, AGAIN, IF WE CAN READ THIS DECIMAL CORRECTLY
WE CAN FIND THE FRACTION FORM.
THIS IS TENTHS, HUNDREDTHS, THOUSANDTHS, TEN-THOUSANDTHS.
THIS IS 15/10,000.
NOW WE DO HAVE A COMMON FACTOR OF FIVE,
SO THIS WOULD BE 3/2000.
AND OUR LAST EXAMPLE, TO CONVERT 2/3 TO A DECIMAL
WE'D TAKE 2 AND DIVIDE BY 3.
2 DIVIDED BY 3 WILL GIVE US A REPEATING DECIMAL.
SO WE NEED TO MAKE SURE WE WRITE THIS CORRECTLY.
THIS IS 0.6 REPEATING, SO WE WOULD HAVE 0.6- WITH A BAR.
AND THEN, AGAIN, TO CONVERT TO A PERCENTAGE
WE HAVE TO TAKE THIS AND MULTIPLY BY 100,
WHICH IS EQUIVALENT TO MOVING THE DECIMAL TO THE RIGHT TWICE.
IF YOU GET CONFUSED BY WHICH DIRECTION TO MOVE THE DECIMAL
JUST THINK IF YOU MULTIPLY BY 100
WE SHOULD GET A LARGER NUMBER THAN WHAT WE START WITH.
SO WE HAVE TO MOVE IT TO THE RIGHT.
AND THEN TO DIVIDE YOU WOULD HAVE A SMALLER NUMBER
SO YOU MOVE TO THE LEFT.
SO IF WE MOVE IT TO THE RIGHT TWICE WE'LL HAVE 66.6 REPEATING.
AND DON'T FORGET THIS IS A PERCENTAGE
SO WE HAVE TO INCLUDE THE PERCENT SIGN.
I HOPE YOU FOUND THIS VIDEO HELPFUL, THANK YOU.