Transcript File

Welcome to the Wonderful
World of ….
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.
Numeral
Digit
Place Value
Face Value
Zero
Place Holder
Value
Periods
Scientific Notation
Expanded Form
Written Form
Standard Form
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").
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.
Numbers Get Bigger
Numbers Get Smaller
•
Ones or
Units
Thousands
Millions
Billions
Trillions
Millionths
Hundred Thousandths
Ten Thousandths
Thousandths
Hundredths
•
Tenths
•
One
Ten
Hundred
Thousand
Ten Thousand
Hundred Thousand
Million
Ten Million
Hundred Million
Billion
Ten Billion
Hundred Billion
Trillion
Ten Trillion
Hundred Trillion
•
Place Values
•
Ones or
Units
Thousands
Millions
Billions
Trillions
Period Name
Millionths
Hundred Thousandths
Ten Thousandths
Thousandths
Hundredths
•
Tenths
•
One
Ten
Hundred
Thousand
Ten Thousand
Hundred Thousand
Million
Ten Million
Hundred Million
Billion
Ten Billion
Hundred Billion
Trillion
Ten Trillion
Hundred Trillion
•
• 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.
Face value
is 4
4 856
Place value is
thousands
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
d) 1 769
e) 92 628
f) 978 856
g) 6 876 432
ten thousands
tens
hundreds
ones
millions
a. What is the face value of the digit in the hundreds
place in each of the following numbers?
Face Value (?)
a) 16 978
b) 45 678 090
c) 69 218
d) 1 769
e) 92 628
f) 978 856
g) 6 876 432
9
0
2
7
6
8
4
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) 45 678
b) 40 000
c) 567 894
c) 4
d) 99 040
d) 40
a. What is the place value of the nine (9) in each of the
following numbers?
b. What is the value of the nine (9) in each of the following
numbers
Value (?)
Place Value (?)
900
a) 12 978
hundreds
b) 45 678 090
c) 79 018
d) 1 009
e) 92 128
f) 978 085
g) 9 876 432
tens
thousands
ones
ten thousands
hundred thousands
millions
90
9 000
9
90 000
900 000
9 000 000
• 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
• Numbers are grouped in sets of three called a
period.
• Each period has three places: the ones, tens
and hundreds.
THOUSANDS
BILLIONS
128 063 245 791
MILLIONS
UNITS
ones, tens, hundreds
Example
4,658,089
Millions
period
Thousands
period
Ones
period
Four million, six hundred fifty-eight thousand, eighty-nine.
Millions
Thousands
9
Thousandths
8
Hundredths
6
Tenths
7
One
3
Ten
5
Hundred
1
Thousand
2
Ten Thousand
Hundred
Thousand
Millions
Ten
Million
Hundred
Million
1

Ones or
Units


1.
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***
34 907 521
When saying large numbers you should:
A) start with the largest place value grouping (period) on the
left hand side.
34 907 521
B) Say the number, then say the grouped place value period
“Thirty four” + million = “Thirty four million”
C) Move to right and say the number in the next period.
34 907 521
“Nine hundred seven” + thousand = “Nine hundred seven
thousand”
D) Keep moving right and say the number in the next period.
34 907 521
“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
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!)
12 001
1.
2.
3.
4.
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.
12 001 = Twelve thousand one
Remember No “and” is used, since we are not using
decimals yet.
1 000 562
When there is no value in one family, you do not
have to include saying that family when writing the
number.
1 000 562 = one million five hundred sixty
two
Notice we did not include the thousands period.
We did not have to include zero thousands
546
8 601
12 897 000
77
1 000 004 600
13 050
155 954 523
3 010
Five hundred forty six
Eight thousand six hundred one
Twelve million eight hundred ninety
seven thousand
Seventy seven
One billion four thousand six hundred
Thirteen thousand fifty
One hundred fifty five million nine
hundred fifty four thousand five
hundred twenty three
Three thousand ten
Six hundred sixty six
nineteen million five hundred
twenty seven thousand
Thirty nine
Two billion thirty thousand sixteen
Three hundred forty one million nine
hundred fifty four thousand eight
hundred eighty eight
nine thousand one
Eight thousand three hundred ten
twenty thousand fifty one
666
19 527 000
39
2 000 030 016
341 954 8888
9 001
8 310
20 051
Write these numbers in words, then try and say them outloud.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
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
Can you say these large numbers out loud?
a). 531
b). 1 256
c). 72 078
d). 450 943
e). 67
f). 72 078
g). 601 345
h). 3 567 980
i). 13 500 001
a). 531
b). 1 256
c). 72 078
d). 450 943
e). 67
f). 72 078
g). 601 345
a). Five hundred thirty one
b). One thousand two hundred fifty six
c). Seventy two thousand seventy eight
d). Four hundred fifty thousand nine
hundred forty three
e). Sixty seven
f). Seventy two thousand seventy eight
g). Six hundred one thousand three
hundred forty five
h). 3 567 980 h). Three million five hundred sixty
seven thousand nine hundred eighty
i). 13 500 001 h). Thirteen million five hundred one
• 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).
Standard
Forms
e. g. 4 856
67
1
78 900 679
• 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.
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.
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 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.
a) 500 + 4
504
672
b) 600 + 70 + 2
62 945
c) 60 000 + 2000 + 900 + 40 + 5
850 364
d) 800 000 + 50 000 + 300 + 60 + 4
e) 3 x 100 000 + 7 x 10 000 + 2 x 1000
372 845
+ 8 x 100 + 4 x 10 + 5 x 1
602 800
f) 6 x 100 000 + 2 x 1000 + 8 x 100
g) 5 x 10 + 6 x 1
56
Practice
Write the following number in expanded form.
a) 568
a) 500 + 60 + 8
b) 10 + 2
b) 12
c) 50 000 + 8 000 + 900
c) 58 900
d) 123 091
d) 100 000 + 20 000 +3 000 + 90 + 1
e) 104 044
e) 100 000 + 4 000 + 40 + 4
f) 1 678 932
f) 1 000 000 + 600 000 + 70 000
g) 12 456
+ 8 000 + 900 + 30 + 2
g) 10 000 + 2 000 + 400 + 50 + 6
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
Form
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.
a) 234
b) 3 405
c) 561 783
d) 1 876 980
Practice
Write the following number in standard, expanded
and written form.
a) 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
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 …..
Remember the Base 10 System?
= 1 000
= 100
= 10
= 10
** USE A
RULER TO
DRAW
YOUR
PICTURES
Representing a Number Using
Base 10
E.g. Using diagrams show the value of 2 322
1 000 + 1 000
+ 100 + 100 + 100
= 2 322
+ 10 + 10
+1+1
Practice
Using the following pictures, write the following numbers in
standard form.
a)
b)
c)
d)
1 111
425
332
3 150
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