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

2. Expectations
- represent, compare, and order whole
numbers 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 Holder
Value
Periods
Scientific Notation
Expanded Form
Written Form
Standard Form

4. 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").

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 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

7. 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!

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

9. Place Value Chart
Numbers Get Bigger Numbers Get Smaller

10. 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

11. 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

12. 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

13. Practice
What is the place value of the six (6) in each of the following numbers?
Place Value (?) a)
thousands b)
hundred thousands c)
ten thousands
Worksheets to Use – Basic Math Skills – Place Value pg. 1
d) 1 769
tens
hundreds e) f)
ones
millions g)

14. Practice
What is the face value of the digit in the hundreds place in each of the following numbers?
Face Value (?) a) 9 b) 2 c) 7
d) 1 769 6 e) 8 f) 4 g)

15. 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) b) c)
c) 4 d)
d) 40

16. 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)
hundreds
900 b)
tens 90 c)
thousands
9 000
d) 1 009
ones 9
90 000 e)
ten thousands
hundred thousands f)
millions g)

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 numbers
Example:
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.

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

19. Written Form

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, hundreds
MILLIONS

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 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***

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 sixty
two

29. A Few Examples of Reading & Writing Whole Numbers
Five hundred forty six
546
8 601
Eight thousand six hundred one
Twelve million eight hundred ninety
seven thousand 77
Seventy seven
One billion four thousand six hundred
13 050
Thirteen thousand fifty
One hundred fifty five million nine
hundred fifty four thousand five
hundred twenty three
3 010
Three thousand ten

30. A Few Examples of Reading & Writing Whole Numbers
Six hundred sixty six
666
nineteen million five hundred
twenty seven thousand 39
Thirty nine
Two billion thirty thousand sixteen
Three hundred forty one million nine
hundred fifty four thousand eight
hundred eighty eight
9 001
nine thousand one
8 310
Eight thousand three hundred ten
twenty thousand fifty one
20 051

31. 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
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

32. When writing a large number put a space between each
period
Canadian Way
345, 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

33. Practice Can you say these large numbers out loud? a). 531 b). 1 256f) g) h) i)

34. 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)
d). Four hundred fifty thousand nine hundred forty three d)
e). 67
e). Sixty seven f)
f). Seventy two thousand seventy eight
g). Six hundred one thousand three hundred forty five g) h)
h). Three million five hundred sixty seven thousand nine hundred eighty
h). Thirteen million five hundred one i)

35. Standard and
Expanded Form

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. g
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?

37. 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.

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 1
Both 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 out
when writing the expanded form.
5 062 =

40. 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
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__ ____ ____ ____ _____

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 1
f) 6 x x x 100
g) 5 x x 1
504
672
62 945 56

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 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) = (7 x ) + (8 x ) + (9 x 1 000) + (1 x 100) + (2 x 10) + (3 x 1)
b) =
Standard
Form
Expanded
Written Form
10 589
(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 eight
12.078
(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. Practice
Write the following number in standard, expanded and written form.
234
3 405

46. Practice
Write the following number in standard, expanded and written form.
234 – 234
- two hundred thirty four
b) – 3 405
- threee thousand four hundred five
c) –
- five hundred sixty one thousand seven hundred
eighty three.

47. Practice
d) –
- one million eight hundred seventy six
thousand nine hundred eighty

48. 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?

49. What about …..
Pictures!!!

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

53. Using four different methods represent the value of the number 3 451.
Problem
Using four different methods represent the value of the number
1. Pictures
2. Expanded Form
3. Written Form
Three thousand four hundred fifty one
4. Scientific Notation
3 x x x x 100