Welcome to the Wonderful World of …. PLACE VALUE!!

Expectations - represent, compare, and order whole numbers to 1 000 000. – demonstrate an understanding of place value in whole numbers from 0.001 to 1 000 000. – read and print in words whole numbers to one hundred thousand.

Vocabulary To Know Numeral Digit Place Value Face Value Zero Place Holder Value Periods Scientific Notation Expanded Form Written Form Standard Form

Digits and Numerals Numerals: A symbol or name that stands for a number. Numerals = Numbers (synonymns) Examples: 3, 49 and twelve are all numerals Digits: 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"). http://www.mathsisfun.com/definitions/digit.html http://www.mathsisfun.com/definitions/numeral.html

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.

Try this In each one of your bags, you have the following place value names. Can you put them in order from smallest to largest? tens thousands hundreds hundred millions millions ten thousands hundred thousands ten millions ones billions

Answers Smallest to Largest Ones Tens Hundreds Thousands ten thousand Hundred thousand Millions Ten millions Hundred millions Billions Did you get them all right? Great Work!

A place value chart helps us to read and understand large numbers.

Place Value Chart Numbers Get Bigger Numbers Get Smaller

Place Value Chart • Trillions Billions Millions Thousands Ones or Units • Hundred Trillion Ten Trillion Trillion Hundred Billion Ten Billion Billion Hundred Million Ten Million Million Hundred Thousand Ten Thousand Thousand Hundred Ten One Tenths Hundredths Thousandths Ten Thousandths Hundred Thousandths Millionths

Place Value Chart • Period Name Place Values Trillions Billions Millions Thousands Ones or Units • Hundred Trillion Ten Trillion Trillion Hundred Billion Ten Billion Billion Hundred Million Ten Million Million Hundred Thousand Ten Thousand Thousand Hundred Ten One Tenths Hundredths Thousandths Ten Thousandths Hundred Thousandths Millionths

Place Value vs. Face Value Face value is 4 Each 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. 4 856 Place value is thousands

Practice What is the place value of the six (6) in each of the following numbers? Place Value (?) a) 16 978 thousands b) 45 678 090 hundred thousands c) 69 218 ten thousands Worksheets to Use – Basic Math Skills – Place Value pg. 1 d) 1 769 tens hundreds e) 92 628 f) 978 856 ones millions g) 6 876 432

Practice What is the face value of the digit in the hundreds place in each of the following numbers? Face Value (?) a) 16 978 9 b) 45 678 090 2 c) 69 218 7 d) 1 769 6 e) 92 628 8 f) 978 856 4 g) 6 876 432

Value The 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) 456 a) 400 b) 40 000 b) 45 678 c) 567 894 c) 4 d) 99 040 d) 40

Practice What 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 numbers Place Value (?) Value (?) a) 12 978 hundreds 900 b) 45 678 090 tens 90 c) 79 018 thousands 9 000 d) 1 009 ones 9 90 000 e) 92 128 ten thousands hundred thousands 900 000 f) 978 085 millions 9 000 000 g) 9 876 432

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 numbers Example: 40 556 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 thousands The 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.

Expanded Form of Numbers Written, Standard and Expanded Form of Numbers

Written Form

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.

128 063 245 791 Periods THOUSANDS BILLIONS UNITS MILLIONS ones, tens, hundreds MILLIONS

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.

 How to Read Whole Numbers 1 2 5 3 7 6 8 9 Ones or Units Millions Hundred Million Million Ten Millions Thousand Hundred Ten Thousand One Tenths Hundredths Thousandths 1 2 5 3 7 6 8 9 Ones or Units Millions Thousands Read the entire number in each period, then add the period name to the end e.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***

How to Read and Write Large Numbers 34 907 521 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” 34 907 521

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. *** 34 907 521 34 907 521

How to Read and Write Large Numbers 34 907 521 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!)

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. 12 001 = Twelve thousand one

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 1 000 562 = one million five hundred sixty two

A Few Examples of Reading & Writing Whole Numbers Five hundred forty six 546 8 601 Eight thousand six hundred one 12 897 000 Twelve million eight hundred ninety seven thousand 77 Seventy seven 1 000 004 600 One billion four thousand six hundred 13 050 Thirteen thousand fifty 155 954 523 One hundred fifty five million nine hundred fifty four thousand five hundred twenty three 3 010 Three thousand ten

A Few Examples of Reading & Writing Whole Numbers Six hundred sixty six 666 nineteen million five hundred twenty seven thousand 19 527 000 39 Thirty nine 2 000 030 016 Two billion thirty thousand sixteen Three hundred forty one million nine hundred fifty four thousand eight hundred eighty eight 341 954 8888 9 001 nine thousand one 8 310 Eight thousand three hundred ten twenty thousand fifty one 20 051

Practice Write these numbers in words, then try and say them outloud. 345 20 45 907 5 678 7 000 12 002 75 802 282 56 2 450 781 a) Three hundred forty five b) Twenty c) Forty Five thousand nine hundred seven d) Five thousand six hundred seventy eight e) Seven thousand f) Twelve thousand two g) Seventy five thousand eight hundred two h) Two hundred eighty two i) Fifty six j) Two million four hundred fifty thousand seven hundred eighty one

When writing a large number put a space between each period 345 905 - Canadian Way 345,905 - American Way Sometimes you will see a larger numbe written with a comma in between the periods. This is the American way of writing larger numbers

Practice Can you say these large numbers out loud? a). 531 b). 1 256 f). 72 078 g). 601 345 h). 3 567 980 i). 13 500 001

Practice a). 531 a). Five hundred thirty one b). 1 256 c). 72 078 b). One thousand two hundred fifty six c). Seventy two thousand seventy eight c). 72 078 d). Four hundred fifty thousand nine hundred forty three d). 450 943 e). 67 e). Sixty seven f). 72 078 f). Seventy two thousand seventy eight g). Six hundred one thousand three hundred forty five g). 601 345 h). 3 567 980 h). Three million five hundred sixty seven thousand nine hundred eighty h). Thirteen million five hundred one i). 13 500 001

Standard and Expanded Form

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. g. 4 856 67 1 78 900 679 Standard Forms Numbers 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?

Expanded Form A 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 combined Zero values are not included.

Expanded Form The number 4856 in expanded form is: Method a) 4000 + 800 + 50 + 6 You may see expanded form written like this: Method b) 4 x 1000 + 8 x 100 + 5 x 10 + 6 x 1 Both methods are correct.

Expanded Form The number 5 062 in expanded form is: 5000 + 000 + 60 + 2 ** Because there is no value for the hundreds place, we can leave the value of the hundreds place out when writing the expanded form. 5 062 = 5000 + 60 + 2

A Trick (or Treat) A trick to writing number in standard form from expanded form is to show the number of lines as there is place values e.g. Write in standard form 50 000 + 6 000 + 700 + 2 50 000 is the largest of the expanded form shown. So we need Five place value lines ___ ____ ____ ____ _____ The face value of the ten thousands place is 5. Put in 5. _5__ ____ ____ ____ _____

(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__

Practice Write the following number in standard form. 500 + 4 600 + 70 + 2 60 000 + 2000 + 900 + 40 + 5 800 000 + 50 000 + 300 + 60 + 4 3 x 100 000 + 7 x 10 000 + 2 x 1000 + 8 x 100 + 4 x 10 + 5 x 1 f) 6 x 100 000 + 2 x 1000 + 8 x 100 g) 5 x 10 + 6 x 1 504 672 62 945 850 364 372 845 602 800 56

Practice Write the following number in expanded form. 568 12 58 900 123 091 104 044 f) 1 678 932 g) 12 456 a) 500 + 60 + 8 b) 10 + 2 c) 50 000 + 8 000 + 900 d) 100 000 + 20 000 +3 000 + 90 + 1 e) 100 000 + 4 000 + 40 + 4 f) 1 000 000 + 600 000 + 70 000 + 8 000 + 900 + 30 + 2 g) 10 000 + 2 000 + 400 + 50 + 6

Standard, Written & Expanded Forms Standard Form: is the number itself. e.g. 1; 15,000; 367 Written Form: is the words for the numbers e.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). 789 123 = (7 x 100 000) + (8 x 10 000) + (9 x 1 000) + (1 x 100) + (2 x 10) + (3 x 1) b) 789 123 = 700 000 + 80 000 + 9 000 + 100 + 20 + 3 Standard Form Expanded Written Form 10 589 (1 x 10 000) + (5 x 100) + (8 x 10) + (9 x 1) Ten thousand five hundred eighty nine 7 589 588 (7 x 1 000 000) + (5 x 100 000) + (8 x 10 000) + (9 x 1 000) + (5 x 100) + (8 x 10) + (8 x 1) Seven million five hundred eighty nine thousand five hundred eighty eight 12.078 (1 x 10) + (2 x 1) + (7 x 0.01) + (8 x 0.001) Twelve AND seventy eight thousandths 0.54669 (5 x 0.1) + (4 x 0.01) + (6 x 0.001) + (6 x 0.0001) + (9 x 0.00001) Fifty four thousand six hundred sixty nine hundred thousandths

Practice Write the following number in standard, expanded and written form. 234 3 405 561 783 1 876 980

Practice Write the following number in standard, expanded and written form. 234 – 234 - 200 + 30 + 4 - two hundred thirty four b) 3 405 – 3 405 - 3000 + 400 + 5 - threee thousand four hundred five c) 561 783 – 561 783 - 500 000 + 60 000 + 1 000 + 700 + 80 + 3 - five hundred sixty one thousand seven hundred eighty three.

Practice d) 1 876 980 – 1 876 980 - 1 000 000 + 800 000 + 70 000 + 6 000 + 900 + 80 - one million eight hundred seventy six thousand nine hundred eighty

Can you think of any other ways to show the value of a number? Representing Numbers How 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?

What about ….. Pictures!!!

Remember the Base 10 System? ** USE A RULER TO DRAW YOUR PICTURES = 1 000 = 10 = 100 = 10

Representing a Number Using Base 10 E.g. Using diagrams show the value of 2 322 1 000 + 1 000 + 100 + 100 + 100 + 10 + 10 + 1 + 1 = 2 322

Practice Using the following pictures, write the following numbers in standard form. a) b) c) d) 1 111 425 332 3 150

Using four different methods represent the value of the number 3 451. Problem Using four different methods represent the value of the number 3 451. 1. Pictures 2. Expanded Form 3000 + 400 + 50 + 1 3. Written Form Three thousand four hundred fifty one 4. Scientific Notation 3 x 103 + 4 x 102 + 5 x 101 + 1 x 100