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

2. 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
x 103

3. 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

4. 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’

5. 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)

6. ***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,
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.
x 103

7. 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
x 103
SCIENTIFIC NOTATION

8. 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)

9. 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
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 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”