- WELCOME TO ANOTHER LESSON ON THE MAYAN NUMBER SYSTEM.
IN THIS LESSON, WE'LL FOCUS ON WRITING BASE 10 NUMBERS
IN BASE 20 AND ALSO AS MAYAN NUMBERS.
REMEMBER THE MAYAN NUMBER SYSTEM IS A BASE 20 SYSTEM.
LET'S BEGIN BY CONSIDERING THE NUMBER 1432 IN DIFFERENT BASES.
WE KNOW IN BASE 10 THE ONE REPRESENTS ONE, ONE THOUSAND
WHICH WE COULD ALSO WRITE AS 1 x 10 TO THE THIRD.
WE KNOW THE FOUR REPRESENTS FOUR HUNDREDS,
WHICH WE CAN ALSO WRITE AS 4 x 10 SQUARED.
THE THREE REPRESENTS THREE TENS
WHICH WE CAN ALSO WRITE AS 3 x 10 TO THE FIRST
AND THE TWO REPRESENTS TWO ONES
WHICH WE COULD ALSO WRITE AS 2 x 10 TO THE ZERO.
SO WE CAN ALWAYS DETERMINE OUR PLACE VALUE BY TAKING THE BASE
AND RAISING IT TO AN INTEGER POWER BASED UPON THE POSITION.
BUT NOW NOTICE IF WE CHANGE THE BASE TO FIVE,
IT DOES CHANGE THE PLACE VALUES AS WE SEE HERE.
FIVE TO THE ZERO WE'D HAVE THE ONES, FIVE TO THE ONE,
WE'D HAVE THE FIVES,
FIVE TO THE TWO WE'D HAVE THE 25'S,
FIVE TO THE THREE WE'D HAVE THE 125S AND SO ON.
SO FOR THE NUMBER 1432 BASE FIVE,
THE ONE HERE REPRESENTS ONE FIVE TO THE THIRD OR 1, 125.
THE FOUR REPRESENTS FOUR, FIVE SQUARED OR 4 25'S.
THE THREE REPRESENTS THREE FIVES OR THREE FIVE TO THE FIRST
AND THE TWO REPRESENTS TWO ONES OR TWO FIVE TO THE ZEROS.
NOTICE HOW 1432 BASE FIVE IS EQUAL TO 242 BASE 10.
NOW LOOKING AT BASE 20, NOTICE HOW WE HAVE THESE COMMAS HERE
AND THAT'S BECAUSE WHEN THE BASE IS 10 OR MORE,
WE DO WANT TO INCLUDE COMMAS BETWEEN THE PLACE VALUES
TO AVOID CONFUSION.
REMEMBER BASE 20 CAN HAVE NUMBERS FROM ZERO TO 19
IN EACH PLACE VALUE.
SO THE PLACE VALUES FOR BASE 20 ARE GIVEN HERE.
SO THIS FIRST ONE REPRESENTS 120 TO THE THIRD OR ONE 8,000.
THE FOUR REPRESENTS FOUR 20 SQUARED OR FOUR 400'S.
THE THREE REPRESENTS THREE 20S, THE TWO REPRESENTS TWO ONES.
SO THIS NUMBER IN BASE 20 IS EQUAL TO 9,662 IN BASE 10.
SO AGAIN WHEN THE BASE OF A NUMBER IS LARGER THAN 10,
WE SEPARATE EACH DIGIT OR EACH PLACE VALUE WITH A COMMA
TO MAKE THE SEPARATION OF THE DIGITS CLEAR.
SO FOR EXAMPLE IN BASE 20,
THIS NUMBER HERE WILL BE WRITTEN 17, 6, 13 IN BASE 20.
NOW FOR A QUICK REVIEW,
REMEMBER THE MAYAN NUMBER SYSTEM IS BASE 20
BUT NUMBERS ARE WRITTEN VERTICALLY FROM THE BOTTOM UP.
SO WE HAVE THE ONE'S PLACE VALUE, THE 20'S, THE 400'S
THE 8,000'S AND SO ON.
AND BECAUSE IT'S A BASE 20 SYSTEM,
WE HAVE TO HAVE SYMBOLS FOR ZERO THROUGH 19
WHICH ARE GIVEN HERE IN THIS TABLE.
SO THIS VIDEO DOES ASSUME YOU'VE ALREADY WATCHED THE FIRST VIDEO
ON THE MAYAN NUMBER SYSTEM.
LET'S TAKE A LOOK AT OUR FIRST EXAMPLE.
WE WANT TO WRITE THE BASE 10 NUMBER 4,896 IN BASE 20
AND THEN ALSO AS A MAYAN NUMBER.
TO WRITE A BASE 10 NUMBER IN A DIFFERENT BASE,
WE CAN USE EITHER THE REMAINDER METHOD OR THE CALCULATOR METHOD.
IN THIS LESSON, WE'LL USE THE CALCULATOR METHOD TO SAVE TIME.
REGARDLESS OF THE METHOD THOUGH IN THE FIRST STEP
WE WANT TO FIND THE HIGHEST POWER OF 20
THAT DIVIDES AT LEAST ONCE INTO 4,896.
SO LOOKING AT OUR POWERS OF 20 HERE,
I NOTICE HOW 20 TO THE THIRD IS TOO LARGE,
SO WE'LL BEGIN BY DIVIDING BY 20 TO THE SECOND OR 400
WHICH MEANS OUR NUMBER IN BASE 20 WILL HAVE THREE PLACE VALUES.
WE'LL FIRST WRITE THIS HORIZONTALLY
AND THEN WRITE IT VERTICALLY AS A MAYAN NUMBER.
SO WE'LL PUT COMMAS BETWEEN THE PLACE VALUES.
AND NOW WE'RE GOING TO TAKE 4,896
AND DIVIDE BY 20 SQUARED OR 400.
WE'LL USE ONLY THE WHOLE NUMBER PART AS OUR FIRST DIGIT
IN THE 400'S PLACE VALUE WHICH WILL BE 12.
SO WE'LL HAVE A 12 HERE,
AND NOW TO FIND THE DIGIT IN THE NEXT PLACE VALUE,
WE'LL SUBTRACT THE WHOLE NUMBER OF 12
AND THEN MULTIPLY BY THE BASE WHICH IS 20 SO x 20 ENTER.
USE THE WHOLE NUMBER PART OF FOUR FOR OUR NEXT DIGIT
WHICH IS HERE.
SUBTRACT THE FOUR AND MULTIPLY IT BY 20 AGAIN.
SO WE HAVE A 16 IN THE ONE'S PLACE VALUE.
SO WHAT WE HAVE FOUND IS THAT 4,896 BASE 10
IS EQUAL TO 12, 4, 16 IN BASE 20.
SO TO WRITE 4,896 BASE 10 AS A MAYAN NUMBER,
WE'LL REPRESENT THESE DIGITS VERTICALLY
USING OUR MAYAN SYMBOLS.
GIVEN HERE.
SO WE'LL START AT THE BOTTOM WITH THE ONES PLACE VALUE.
SO FOR 16 REMEMBER EACH BAR IS FIVE,
SO WE'LL HAVE FIVE, 10, 15,
AND ONE DOT, THAT'S 16 IN THE ONE'S PLACE VALUE.
WE HAVE A FOUR IN THE 20'S PLACE VALUE,
FOUR WOULD JUST BE FOUR DOTS
SO WE LEAVE A SPACE AND PUT FOUR DOTS HERE.
AND THEN FINALLY IN THE 400'S PLACE VALUE WE HAVE 12
SO WE'D HAVE FIVE, 19 AND TWO DOTS.
THIS WOULD BE THE GIVEN NUMBER OF A MAYAN NUMBER
TO VERIFY THIS IS CORRECT
WE COULD WRITE THIS OUT USING PLACE VALUES
WHICH I'VE ALREADY DONE HERE TO SAVE SOME TIME.
WE HAVE 12 20 SQUAREDS FOUR 20 TO THE FIRST
AND 16 20 TO THE ZEROS GIVING US A VALUE IN BASE 10 OF 4,896.
NOW LET'S TAKE A LOOK AT A SECOND EXAMPLE.
WE WANT TO WRITE THE BASE 10 NUMBER 84,185 IN BASE 20
AND AS A MAYAN NUMBER.
AGAIN THE FIRST STEP IS TO FIND THE HIGHEST POWER OF 20
THAT DIVIDES AT LEAST ONCE INTO 84,185.
NOTICE HOW 20 TO THE FOURTH WOULD BE TOO LARGE
SO WE'LL DIVIDE BY 20 TO THE THIRD OR 8,000
WHICH MEANS OUR NUMBER WILL HAVE ONE, TWO, THREE, FOUR DIGITS
OR FOUR PLACE VALUES
AND SO ONE, TWO, THREE, FOUR, SEPARATE IT WITH COMMAS,
AND NOW WE'LL GO BACK TO THE CALCULATOR 84,185
DIVIDED BY 8,000, ENTER.
IF THE WHOLE NUMBER PART IS GREATER THAN OR EQUAL TO 20,
WE KNOW WE DIDN'T USE THE CORRECT POWER OF 20
TO DIVIDE BY.
SO WE'LL USE THE WHOLE NUMBER OF 10
TO PUT INTO THE 8,000 PLACE VALUE,
NOW SUBTRACT 10 AND MULTIPLY BY THE BASE OF 20
TO FIND THE NEXT DIGIT.
SO - 10 ENTER, x THE BASE OF 20
SO THE NEXT DIGIT IS ALSO GOING TO BE 10.
SUBTRACT THE WHOLE NUMBER, OF 10, MULTIPLY IT BY 20 AGAIN.
THE NEXT DIGIT WOULD BE NINE,
SUBTRACT NINE AND MULTIPLY IT BY 20.
THE LAST DIGIT IS FIVE WHICH MEANS 84,185 BASE 10
IS EQUAL TO 10, 10, 9, 5 BASE 20.
-- A MAYAN NUMBER WE'LL NOW WRITE THIS VERTICALLY
STARTING WITH THE ONES GOING UP TO THE 8,000'S PLACE VALUE.
WE HAVE A FIVE IN THE ONE'S PLACE VALUE
SO WE HAVE A HORIZONTAL BAR.
THERE'S FIVE, IN THE 20'S WE HAVE NINE
SO WE HAVE A HORIZONTAL BAR AND FOUR DOTS.
THERE'S NINE.
THEN WE HAVE 10 IN THE 400'S PLACE VALUE, FIVE, 10,
AND WE ALSO HAVE 10 IN THE 8,000 PLACE VALUE FIVE AND TEN.
HERE'S THE NUMBER WRITTEN AS A MAYAN NUMBER.
AND AGAIN TO VERIFY THIS IS CORRECT,
WE CAN ALWAYS EXPAND THIS USING THE CORRECT PLACE VALUES
WHICH I'VE ALREADY DONE HERE,
10, 20 TO THE THIRDS 10 20 SQUAREDS,
NINE 20 TO THE FIRST AND FIVE 20 TO THE ZEROS.
GIVING US 84,185 IN BASE 10.
I HOPE YOU FOUND THIS HELPFUL.