Welcome to the Wonderful World of ….

Expectations

- represent, compare, and order wholenumbers 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.

NumeralDigitPlace ValueFace ValueZeroPlace HolderValuePeriodsScientific NotationExpanded FormWritten FormStandard 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.

• In 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

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

Trillions Billions Millions Thousands

Ones or Units

•

Hundre

d T

rillion

Ten T

rillion

Trillio

n

Hundre

d B

illion

Ten B

illion

Billio

n

Hundre

d M

illion

Ten M

illion

Millio

n

Hundre

d T

housa

nd

Ten T

housa

nd

Thousa

nd

Hundre

d

Ten

One

•

Tenth

s

Hundre

dth

s

Thousa

ndth

s

Ten T

housa

ndth

s

Hundre

d

Thousa

ndth

s

Millio

nth

s

•

•

Trillions Billions Millions Thousands

Ones or Units

•

Hundre

d T

rillion

Ten T

rillion

Trillio

n

Hundre

d B

illion

Ten B

illion

Billio

n

Hundre

d M

illion

Ten M

illion

Millio

n

Hundre

d T

housa

nd

Ten T

housa

nd

Thousa

nd

Hundre

d

Ten

One

•

Tenth

s

Hundre

dth

s

Thousa

ndth

s

Ten T

housa

ndth

s

Hundre

d

Thousa

ndth

s

Millio

nth

s

•

•

Place ValuesPeriod Name

• 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

Face value is 4

Place value is

thousands

What is the place value of the six (6) in each of the following numbers?

a) 16 978

thousands

b) 45 678 090

hundred thousandsc) 69

218ten thousandsd) 1 769

e) 92 628f) 978 856

g) 6 876 432

Place Value (?)

tens

hundreds

onesmillions

a. What is the face value of the digit in the hundreds place in each of the following numbers?

a) 16 978

9

b) 45 678 090c) 69 218

0

8

d) 1 769

e) 92 628f) 978 856

g) 6 876 432

Face Value (?)

2

6

4

7

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

c) 567 894

b) 45 678

d) 99 040

a) 400b) 40 000

c) 4

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

a) 12 978

900hundredsb) 45 678

090tens

c) 79 018

90

thousands

900 000

d) 1 009

e) 92 128f) 978 085

g) 9 876 432

Place Value (?)

Value (?)

9 000

90 000

9 000 000

9ones

ten thousandshundred

thousandsmillions

• 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.

128 063 245 791

THOUSANDS

MILLIONS

BILLIONS

UNITSones, tens, hundreds

Example4,658,089Millions period

Thousands period

Ones period

Four million, six hundred fifty-eight thousand, eighty-nine.

Hundre

d

Millio

n

Ten

Millio

n

Millio

ns

Hundre

dThousa

nd

Ten T

housa

nd

Thousa

nd

Hundre

d

Ten

One

Tenth

s

Hundre

dth

s

Thousa

ndth

s

1 2 1 5 3 7 6 8 9

Millions ThousandsOnes or Units

1. Read 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***

When saying large numbers you should:

A)start with the largest place value grouping (period) on the left hand side.

B)Say the number, then say the grouped place value period

“Thirty four” + million = “Thirty four million”

34 907 521

34 907 521

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

34 907 521Now you can add all the names together.

“Thirty-four million nine hundred seven five hundred twenty-one”

ALERTALERT“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.Say the number in the left period first.2.Next, add the period name to the end of it. 3.Then say the number in the period to its right.4.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

1 000 562

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

Five hundred forty six546

8 601

12 897 000

3 010

77

1 000 004 600

155 954 523

13 050

Eight thousand six hundred one

Thirteen thousand fifty

Seventy seven

Three thousand ten

One billion four thousand six hundred

One hundred fifty five million nine hundred fifty four thousand five hundred twenty three

Twelve million eight hundred ninety seven thousand

Six hundred sixty six 666

19 527 000

39

2 000 030 016

341 954 8888

9 001

8 310

20 051

Eight thousand three hundred ten

twenty thousand fifty one

Thirty nine

nine thousand one

Two billion thirty thousand sixteen

Three hundred forty one million nine hundred fifty four thousand eighthundred eighty eight

nineteen million five hundred twenty seven thousand

Write these numbers in words, then try and say them outloud.

a)345b)20c)45 907d)5 678e)7 000f)12 002 g)75 802h)282i)56j)2 450 781

b) Twentyc) Forty Five thousand nine hundred seven

e) Seven thousand

g) Seventy five thousand eight hundred two

f) Twelve thousand two

i) Fifty six

h) Two hundred eighty two

j) Two million four hundred fifty thousand seven hundred eighty one

d) Five thousand six hundred seventy eight

a) Three hundred forty five

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

a). 531 b). 1 256c). 72 078

g). 601 345

d). 450 943

f). 72 078

e). 67

h). 3 567 980

i). 13 500 001

Can you say these large numbers out loud?

a). 531 b). 1 256

a). Five hundred thirty one

c). 72 078c). Seventy two thousand seventy eight

g). 601 345

d). 450 943

f). 72 078

e). 67

h). 3 567 980

b). One thousand two hundred fifty six

d). Four hundred fifty thousand nine hundred forty threee). Sixty seven

g). Six hundred one thousand three hundred forty five

f). Seventy two thousand seventy eight

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).

e. g. 4 856 67 1 78 900 679

Standard Forms

• 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.

Method b) 4 x 1000 + 8 x 100 + 5 x 10 + 6 x 1

Method a) 4000 + 800 + 50 + 6

The number 4856 in expanded form is:

You may see expanded form written like this:

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 needFive 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__

PracticeWrite the following number in standard form.a)500 + 4b)600 + 70 + 2c)60 000 + 2000 + 900 + 40 + 5d)800 000 + 50 000 + 300 + 60 + 4e)3 x 100 000 + 7 x 10 000 + 2 x 1000 + 8 x 100 + 4 x 10 + 5 x 1f) 6 x 100 000 + 2 x 1000 + 8 x 100 g) 5 x 10 + 6 x 1

602 800

504

850 364

672

62 945

372 845

56

PracticeWrite the following number in expanded form.a)568b)12c)58 900d)123 091e)104 044f) 1 678 932g) 12 456

f) 1 000 000 + 600 000 + 70 000 + 8 000 + 900 + 30 + 2

a) 500 + 60 + 8

d) 100 000 + 20 000 +3 000 + 90 + 1

b) 10 + 2

c) 50 000 + 8 000 + 900

e) 100 000 + 4 000 + 40 + 4

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

StandardForm

ExpandedForm

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

PracticeWrite the following number in standard, expanded and written form.a)234

b)3 405

c)561 783

d)1 876 980

Practice

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.

Write the following number in standard, expanded and written form.

Practiced) 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 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?

What about …..

Remember the Base 10 System?

= 100

= 10

= 10

= 1 000

** 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 + 10 + 10 + 1 + 1

= 2 322

PracticeUsing the following pictures, write the following numbers in standard form.

a)

b)

c)

d)

1 111

425

332

3 150

ProblemUsing four different methods represent the value of the

number 3 451.

1. Pictures

3. Written Form

Three thousand four hundred fifty one

4. Scientific Notation

3 x 103 + 4 x 102 + 5 x 101 + 1 x 100

2. Expanded Form

3000 + 400 + 50 + 1