Presentation on theme: "Welcome to the Wonderful World of …."— Presentation transcript:
1 Welcome to the Wonderful World of …. PLACE VALUE!!
2 Expectations- represent, compare, and order wholenumbers to– demonstrate an understanding of place value in whole numbers from to– read and print in words whole numbers to one hundred thousand.
3 Vocabulary To Know Numeral Digit Place Value Face Value Zero Place HolderValuePeriodsScientific NotationExpanded FormWritten FormStandard Form
4 Digits and NumeralsNumerals: A symbol or name that stands for a number. Numerals = Numbers (synonymns)Examples: 3, 49 and twelve are all numeralsDigits: A symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numbers. Example: the numeral 153 is made up of 3 digits ("1", "5" and "3").
5 A place value chart helps us to read and understand large numbers. Place Value is the value of a digit determined by its position in a number.A place value chart helps us to read and understand large numbers.
6 Try thisIn each one of your bags, you have the following place value names. Can you put them in order from smallest to largest?tens thousandshundreds hundred millionsmillions ten thousandshundred thousands ten millionsones billions
7 Answers Smallest to Largest Ones Tens Hundreds Thousands ten thousand Hundred thousandMillionsTen millionsHundred millionsBillionsDid you get them all right?Great Work!
8 A place value chart helps us to read and understand large numbers.
9 Place Value ChartNumbers Get Bigger Numbers Get Smaller
10 Place Value Chart • Trillions Billions Millions Thousands Ones or Units•Hundred TrillionTen TrillionTrillionHundred BillionTen BillionBillionHundred MillionTen MillionMillionHundred ThousandTen ThousandThousandHundredTenOneTenthsHundredthsThousandthsTen ThousandthsHundred ThousandthsMillionths
11 Place Value Chart • Period Name Place Values Trillions Billions MillionsThousandsOnes or Units•Hundred TrillionTen TrillionTrillionHundred BillionTen BillionBillionHundred MillionTen MillionMillionHundred ThousandTen ThousandThousandHundredTenOneTenthsHundredthsThousandthsTen ThousandthsHundred ThousandthsMillionths
12 Place Value vs. Face Value Face value is 4Each digit in a number has a place value , a face value and a value.In the number 4 856, the digit 4 is in the thousands place value.Meaning the place value is thousands.The number you see (4) is the face value.4 856Place value is thousands
13 PracticeWhat is the place value of the six (6) in each of the following numbers?Place Value (?)a)thousandsb)hundred thousandsc)ten thousandsWorksheets to Use – Basic Math Skills – Place Value pg. 1d) 1 769tenshundredse)f)onesmillionsg)
14 PracticeWhat is the face value of the digit in the hundreds place in each of the following numbers?Face Value (?)a)9b)2c)7d) 1 7696e)8f)4g)
15 ValueThe value of a place is how much the digit in that place is worth.Example: What is the value of the digit four (4) in each number?a) 456a) 400b)b)c)c) 4d)d) 40
16 PracticeWhat is the place value of the nine (9) in each of the following numbers?What is the value of the nine (9) in each of the following numbersPlace Value (?)Value (?)a)hundreds900b)tens90c)thousands9 000d) 1 009ones990 000e)ten thousandshundred thousandsf)millionsg)
17 Zero: The Hero Example: 40 556 Zero is used as a place holder to show there is a place value, but there is no value to that place.Zeros are put in to the right of numbersExample:Zero is the place holder for the thousands place because there is no value for it, but we still need to show that there is a place for the thousandsThe idea of place value is at the heart of our number system. First, however, a symbol for nothing--our zero--had to be invented. Zero "holds the place" for a particular value, when no other digit goes in that position. For example, the number "100" in words means one hundred, no tens, and no ones. Without a symbol for nothing, our decimal number system wouldn't work.
18 Expanded Form of Numbers Written, Standard andExpanded Form of Numbers
20 How to Read and Write Large Numbers Numbers are grouped in sets of three called a period.Each period has three places: the ones, tens and hundreds.The periods are: the billions period, millions period, thousands period etc. Each period has three places within it. The ones, tens and hundreds.
21 128 063 245 791 Periods THOUSANDS BILLIONS UNITS MILLIONS ones, tens, hundredsMILLIONS
22 4,658,089 Example Millions period Thousands period Ones period Four million, six hundred fifty-eight thousand, eighty-nine.Beginning with the ones place at the right, each place value is multiplied by increasing powers of 10. For example, the value of the first place on the right is "one", the value of the place to the left of it is "ten," which is 10 times 1. The place to the left of the tens place is hundreds, which is 10 times 10, and so forth.For easier readability, commas are used to separate each group of three digits, which is called a period. When a number is written in this form, it is said to be in "standard form." Americans use commas, Canadians just use a space.
23 How to Read Whole Numbers 1 2 5 3 7 6 8 9 Ones or Units Millions Hundred MillionMillionTenMillionsThousandHundredTen ThousandOneTenthsHundredthsThousandths12537689Ones or UnitsMillionsThousandsRead the entire number in each period, then add the period name to the ende.g. “One hundred twenty one” million“Five hundred thirty seven” thousand“Six hundred eighty nine”One hundred twenty one million, five hundred thirty seven thousand, six hundred eighty nine.***Notice no AND was used to read whole numbers***
24 How to Read and Write Large Numbers When saying large numbers you should:start with the largest place value grouping (period) on the left hand side.Say the number, then say the grouped place value period“Thirty four” + million = “Thirty four million”
25 How to Read and Write Large Numbers C) Move to right and say the number in the next period.“Nine hundred seven” + thousand = “Nine hundred seven thousand”D) Keep moving right and say the number in the next period.“Five hundred twenty one” + hundreds = “Five hundred twenty one”*** the period name for the hundreds can be dropped when saying or writing the number. ***
26 How to Read and Write Large Numbers Now you can add all the names together.“Thirty-four million nine hundred seven five hundred twenty-one”ALERT“AND” is only said or written when there is a decimal.DO NOT say “and” if there isn’t a decimal. ( It’s hard, but you can do it!)
27 Example #1 12 001 12 001 = Twelve thousand one Say the number in the left period first.Next, add the period name to the end of it.Then say the number in the period to its right.We can leave the family name hundreds off.Remember No “and” is used, since we are not using decimals yet.= Twelve thousand one
28 Example #2 1 000 562 1 000 562 = one million five hundred sixty two When there is no value in one family, you do not have to include saying that family when writing the number.Notice we did not include the thousands period. We did not have to include zero thousands= one million five hundred sixtytwo
29 A Few Examples of Reading & Writing Whole Numbers Five hundred forty six5468 601Eight thousand six hundred oneTwelve million eight hundred ninetyseven thousand77Seventy sevenOne billion four thousand six hundred13 050Thirteen thousand fiftyOne hundred fifty five million ninehundred fifty four thousand fivehundred twenty three3 010Three thousand ten
30 A Few Examples of Reading & Writing Whole Numbers Six hundred sixty six666nineteen million five hundredtwenty seven thousand39Thirty nineTwo billion thirty thousand sixteenThree hundred forty one million ninehundred fifty four thousand eighthundred eighty eight9 001nine thousand one8 310Eight thousand three hundred tentwenty thousand fifty one20 051
31 Practice Write these numbers in words, then try and say them outloud. 3452045 9075 6787 00012 00275 80228256a) Three hundred forty fiveb) Twentyc) Forty Five thousand nine hundred sevend) Five thousand six hundred seventy eighte) Seven thousandf) Twelve thousand twog) Seventy five thousand eight hundred twoh) Two hundred eighty twoi) Fifty sixj) Two million four hundred fifty thousand seven hundred eighty one
32 When writing a large number put a space between each periodCanadian Way345, American WaySometimes you will see a larger numbe written with a comma in between the periods. This is the American way of writing larger numbers
33 Practice Can you say these large numbers out loud? a). 531 b). 1 256 f)g)h)i)
34 Practice a). 531 a). Five hundred thirty one b). 1 256 c). 72 078 b). One thousand two hundred fifty sixc). Seventy two thousand seventy eightc)d). Four hundred fifty thousand nine hundred forty threed)e). 67e). Sixty sevenf)f). Seventy two thousand seventy eightg). Six hundred one thousand three hundred forty fiveg)h)h). Three million five hundred sixty seven thousand nine hundred eightyh). Thirteen million five hundred onei)
36 Standard Form Standard Forms e. g. 4 856 67 1 78 900 679 When numbers are presented in numerical digits, it is called the standard form of a number.a number is written using digits and place value (the regular way to write numbers).e. gStandard FormsNumbers can be represented in many ways, but standard form is usually the easiest and shortest way. Here are some numbers expressed in different forms, with their standard form shown alongside. Which form do you think is the best?
37 Expanded FormA number is written as a sum using the place and value of each digit.This means writing, separately, the value of each digit in the each place value the number.The values must be written from largest to smallest, and have an addition sign to shown they are combinedZero values are not included.
38 Expanded Form The number 4856 in expanded form is: Method a)You may see expanded form written like this:Method b) 4 x x x x 1Both methods are correct.
39 Expanded Form The number 5 062 in expanded form is: ** Because there is no value for the hundreds place,we can leave the value of the hundreds place outwhen writing the expanded form.5 062 =
40 A Trick (or Treat)A trick to writing number in standard form from expandedform is to show the number of lines as there is place valuese.g. Write in standard formis the largest of the expanded form shown. So we needFive place value lines___ ____ ____ ____ _____The face value of the ten thousands place is 5. Put in 5._5__ ____ ____ ____ _____
41 (Continued) Write in standard form 50 000 + 6 000 + 700 + 2 The face value of the thousands place is 6. Put in 6._5__ __6__ ____ ____ _____The face value of the hundreds place is 7. Put in 7._5__ __6__ __7__ ____ _____The face value of the tens place is 0, because there is no value for the tens place shown. Put in 0._5__ __6__ __ 7 _ __0_ _____The face value of the hundreds place is 2. Put in 2._5__ __6__ __7__ __ 0 __ __2__
42 Practice Write the following number in standard form. 500 + 4 3 x x x 1000+ 8 x x x 1f) 6 x x x 100g) 5 x x 150467262 94556
43 Practice Write the following number in expanded form. 568 12 58 900 f)g)a)b)c)d)e)f)g)
44 Standard, Written & Expanded Forms Standard Form: is the number itself.e.g ; 15,000;Written Form: is the words for the numberse.g. one; sixty; twelve million; two hundred eighty thousand ten.Expanded Form: is writing a number by separating it into each of its place values.Two Versions:a) = (7 x ) + (8 x ) + (9 x 1 000) + (1 x 100) + (2 x 10) + (3 x 1)b) =StandardFormExpandedWritten Form10 589(1 x ) + (5 x 100) + (8 x 10) + (9 x 1)Ten thousand five hundred eighty nine(7 x ) + (5 x ) + (8 x ) (9 x 1 000) + (5 x 100) + (8 x 10) + (8 x 1)Seven million five hundred eighty nine thousand five hundred eighty eight12.078(1 x 10) + (2 x 1) + (7 x 0.01) + (8 x 0.001)Twelve AND seventy eight thousandths(5 x 0.1) + (4 x 0.01) + (6 x 0.001) + (6 x ) + (9 x )Fifty four thousand six hundred sixty nine hundred thousandths
45 PracticeWrite the following number in standard, expanded and written form.2343 405
46 PracticeWrite the following number in standard, expanded and written form.234 – 234- two hundred thirty fourb) – 3 405- threee thousand four hundred fivec) –- five hundred sixty one thousand seven hundredeighty three.
47 Practiced) –- one million eight hundred seventy sixthousand nine hundred eighty
48 Can you think of any other ways to show the value of a number? Representing NumbersHow many ways can you think of to represent the value of a number?- Standard form (numbers)- Written form (words)- Expanded form (values)- Scientific Notation (values)- Money (values)Can you think of any other ways to show the value of a number?
50 Remember the Base 10 System? ** USE A RULER TO DRAW YOUR PICTURES= 1 000= 10= 100= 10
51 Representing a Number Using Base 10 E.g. Using diagrams show the value of= 2 322
52 PracticeUsing the following pictures, write the following numbers in standard form.a)b)c)d)1 1114253323 150
53 Using four different methods represent the value of the number 3 451. ProblemUsing four different methods represent the value of the number1. Pictures2. Expanded Form3. Written FormThree thousand four hundred fifty one4. Scientific Notation3 x x x x 100