MAKING SENSE OF NUMBER SENSE DUFF’S MATH STUFF… MAKING SENSE OF NUMBER SENSE LESSON 3 Forms of a number

4 WAYS TO EXPRESS A NUMBER NUMBER FORM EXAMPLE STANDARD FORM 4,713.5 WRITTEN FORM FOUR THOUSAND SEVEN HUNDRED THIRTEEN AND FIVE TENTHS EXPANDED FORM (4 x 1000) + (7 x 100) + (1 x 10) + (3 x1) + (5 x 1/10) SCIENTIFIC NOTATION 4.7135 x 103

ARE EXPRESSED IN STANDARD FORM IN EVERY-DAY ENGLISH, THE WORD “STANDARD” MEANS THE USUAL WAY WE DO THINGS… THE ‘USUAL’ WAY TO WRITE NUMBERS IN MATH IS USING DIGITS: 3,206 AND 12,047.9 ARE EXPRESSED IN STANDARD FORM

WRITTEN FORM WHEN NUMBERS ARE EXPRESSED IN WORDS, THIS IS CALLED WRITTEN FORM TO THE LEFT OF THE DECIMAL POINT, EVERY 3 NUMBERS ARE SEPARATED BY COMMAS; EACH GROUP OF 3 NUMBERS IS CALLED A PERIOD WHEN WRITING NUMBERS IN WORDS, WE INSERT THE NAME OF THE PERIOD AT EACH COMMA TO THE RIGHT OF THE DECIMAL POINT, WE READ/WRITE NUMBERS IN WORDS JUST LIKE WE READ ON THE LEFT THE LAST WORD SHOULD BE THE PLACE VALUE OF THE LAST DECIMAL DIGIT THE WORD AND IS USED TO REPRESENT THE DECIMAL POINT, AND SHOULD NOT APPEAR ANYWHERE ELSE IN THE NAME OF THE NUMBER 3,206 IS ‘THREE THOUSAND TWO HUNDRED SIX’ 12,047.9 IS ‘TWELVE THOUSAND FORTY SEVEN AND NINE TENTHS’

PLACE VALUES ARE THE KEY TO WRITING NUMBERS IN EXPANDED FORM MILLIONS THOUSANDS UNITS PERIOD DECIMALS 100 MILLIONS 10 MILLIONS 1 MILLIONS 100 THOUSANDS 10 THOUSANDS 1 THOUSANDS HUNDREDS TENS ONES DECIMAL POINT TENTHS HUNDREDTHS THOUSANDTHS 2 7 6 5 . 4 8 WRITE EACH DIGIT AS A PRODUCT OF ITS PLACE VALUE AND TAKE THE SUM... DECIMAL PLACE VALUES ARE EXPRESSED AS FRACTIONS. (2 x 10,000) + (7 x 1,000) + (6 x 10) + (5 x 1) + (4 x 1/10) + (8 x 1/100)

***DO NOT DELETE OR REARRANGE ANY DIGITS*** SCIENTIFIC NOTATION SCIENTISTS HAVE TO WORK WITH VERY LARGE WHOLE NUMBERS AND VERY SMALL DECIMAL NUMBERS…THEY USE SCIENTIFIC NOTATION TO SIMPLIFY THE WAY THESE KINDS OF NUMBERS LOOK LOCATE THE DECIMAL POINT AND MOVE IT TO THE LEFT UNTIL THERE IS EXACTLY ONE COUNTING DIGIT BEFORE IT. ***DO NOT DELETE OR REARRANGE ANY DIGITS*** 6,750.109 6.750109 YOU WILL MULTIPLY THIS NEW NUMBER BY A POWER OF TEN (A BASE OF TEN WITH AN EXPONENT)…THE EXPONENT WILL BE THE NUMBER OF PLACES YOU MOVED THE DECIMAL POINT. THE DECIMAL POINT MOVED 3 PLACES, SO THE EXPONENT ON THE POWER OF TEN WILL BE 3. 6.750109 x 103

ONE NUMBER…FOUR WAYS !!! 5,401.027 WRITTEN FORM 5.401027 x 103 STANDARD FORM WRITTEN FORM FIVE THOUSAND FOUR HUNDRED ONE AND TWENTY-SEVEN THOUSANDTHS (5 x 1000) + (4 x 100) + (1 x 1) + (2 x 1/100) + (7 x 1/1000) EXPANDED FORM 5.401027 x 103 SCIENTIFIC NOTATION

LESSON 3 VOCABULARY REVIEW TERM DEFINITION DIGIT A SINGLE NUMBER WITHIN A LARGE NUMBER (THE DIGITS 5 AND 7 MAKE THE NUMBER 57) PLACE VALUE THE VALUE OF A PARTICULAR DIGIT ACCORDING TO ITS POSITION WITHIN A NUMBER (IN 702.5, 2 IS IN THE ‘ONES’ PLACE AND 5 IS IN THE ‘TENTHS’ PLACE) STANDARD FORM A NUMBER EXPRESSED ENTIRELY IN DIGITS (THE STANARD FORM OF 6,205.4 IS ‘6,205.4) PERIOD SETS OF 3 DIGITS SEPARATED BY COMMAS IN LARGE WHOLE NUMBERS (IN 12,317,465 ‘465’ IS IN THE UNITS PERIOD, ‘317’ IS IN THE THOUSANDS PERIOD) WRITTEN FORM A NUMBER EXPRESSED IN WORDS, WITH THE WORD “AND” SIGNIFYING THE LOCATION OF THE DECIMAL POINT AND THE LAST DECIMAL PLACE VALUE WRITTEN AS THE LAST WORD, IF NECESSARY (THE WRITTEN FORM OF 6,205.4 IS SIX THOUSAND TWO HUNDRED FIVE AND FOUR TENTHS) DECIMAL SYMBOL USED TO SEPARATE WHOLE DIGITS FROM FRACTIONAL VALUES IN A SINGLE NUMBER (IN 4.7, THE WHOLE NUMBER IS 4 AND 7/10 IS SHOWN BY INSERTING THE DECIMAL AND PLACING THE 7 AFTER IT, IN THE TENTHS PLACE)

LESSON 3 VOCABULARY REVIEW TERM DEFINITION ‘AND’ IDENTIFIES THE LOCATION OF THE DECIMAL POINT WHEN NUMBERS ARE IN WRITTEN FORM (EIGHT HUNDRED SEVEN AND FOUR TENTHS LOOKS LIKE 807.4) EXPANDED FORM TO WRITE EACH DIGIT OF A GIVEN NUMBER AS A PRODUCT OF ITS PLACE VALUE AND TAKE THE SUM … 347 IS WRITTEN AS (3 X 100) + (4 X 10) + (7 X 1) OR 300 + 40 + 7 PRODUCT SOLUTION TO A MULTIPLICATION PROBLEM (4X7 IS 28 OR THE PRODUCT OF 4 AND 7 IS 28) SCIENTIFIC NOTATION A NUMBER EXPRESSED AS THE PRODUCT OF A DECIMIAL NUMBER (GREATER THAN OR EQUAL TO 1 AND LESS THAN 10) AND A POWER AND TEN (6.71 X 104 IS WRITTEN IN SCIENTIFIC NOTATION; 67.1 X 103 OR 6.7 X 10000 ARE NOT) POWER OF TEN AN EXPRESSION IN WHICH TEN IS A BASE NUMBER; POWERS OF TEN ARE IMPORTANT WHEN EXPRESSING VALUES IN SCIENTIFIC NOTATION CONVERT TO TRANSLATE BETWEEN DIFFERENT FORMS OF A NUMBER; “CHANGE”