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M5.A.1.1.1 Use expanded notation to represent whole numbers or decimals (whole numbers less than 10,000,000 and decimals through hundredths).

- Expanded Form – a way to write numbers that shows the place value of each digit.

How do I write a whole number using expanded notation?

**When doing expanded form…. We are breaking a number down in pieces.

**The pieces are the numbers in the problem and their place values.

248

How many ones are there?

How many tens are there?

How many hundreds are there?

The expanded form is:

4,367 =

4,000 +

300 +

60 +

7 +

4,000 + 300 + 60 + 7 +

2,000

300

+ 9

2,309

2,000 + 300 + 9+

16,823 =

10,000 +

6,000 +

800 +

20 +

3+

10,000 + 6,000 + 800 + 20 + 3

75,348 =

8,656 =

52,678 =

49,631 =

42,765 =

783,214 =

What if you are given:

400 + 70 + 2

Expanded Notation:2000 + 300 + 9

Notice there are no tens! We do not include 0 in our expanded notation. But, we DO include it when writing the number.

2,309

This shows that there are no tens in this number.

2,000 + 900 + 30 + 5 =

20,000 +7,000 + 100 + 20 + 2 =

4,000 + 500 + 40 + 3 =

8,000 + 400 + 50 + 7 =

30,000 + 6,000 + 300 + 80 + 5 =

10,000 + 2,000 + 500 + 4 =

What does this mean??

(5 x 1,000) + (3 x 100) + (4 x 10) + (7 x 1)

5,000 + 300 + 40 + 7

Multiply each number by 1 and tack on the 0’s at the end.

Let’s check it out again…

(4 x 1,000,000) + (3 x 10,000) + (7 x 1,000) + (4 x 100) + (5 x 10) + (9 x 1)

(9 x 10,000) + (4 x 1,000) + (3 x 100) + (2 x 10) + (4 x 1) =

(8 x 100,000) + (5 x 1,000) + (4 x 100) + (8 x 10) + (6 x 1)=

(4 x 1,000) + (6 x 100) + (8 x 10) + (2 x 1) =

(9 x 1,000,000) + (8 x 10,000) + (5 x 1,000) + (3 x 100) + (7 x 10) + (6 x 1) =

(5 x 10,000) + (4 x 1,000) + (9 x 100) + ( 3 x 10) + (7 x 1) =

(7 x 100,000) + (3 x 10,000) + (8 x 100) + (4 x 10) + (9 x 1) =

248.14

How many ones are there?

How many tens are there?

How many hundreds are there?

How many tenths are there?

How many hundreths are there?

The expanded form is:

67.32

60 + 7 + 0.3 + 0.02

tens + ones + tenths + hundredths

4,367.32

4,000 + 300 + 60 + 7 + 0.3 + 0.02

thousands + hundreds + tens + ones + tenths + hundredths

4,367.32

4,000.00

300.00

60.00

7.00

0.30

+ 0.02

4,367.32

Line up the ONES place in all of the numbers to add them together.

16,823.94

75,348.12 =

8,656.43 =

52,678.91 =

49,631.32 =

42,765.57 =

783,214.41 =

What if you are given:

400 + 70 + 2 + 0.2 + 0.05

2,000+ 300 + 90 + 4 + 0.1 + 0.03

2,000 + 900 + 30 + 5 + 0.8 +0.03 =

20,000 +7,000 + 100 + 20 + 2 + 0.7 + 0.04 =

4,000 + 500 + 40 + 3 + 0.6 + 0.09 =

8,000 + 400 + 50 + 7 + 0.3 + 0.07=

30,000 + 6,000 + 300 + 80 + 5 + 0.4 +0.02 =

7,000 + 800 + 40 + 1 + 0.9 + 0.04 =

What does this mean??

(5 x 1,000) + (3 x 100) + (4 x 10) + (7 x 1) + (5 x 0.1) + (6 x 0.01)

5,000 + 300 + 40 + 7 + 0.5 + 0.06

5,347.56

Multiply each number by 1 and include any 0s that are before or after.

Let’s check it out again…

(4 x 1,000,000) + (3 x 10,000) + (7 x 1,000) + (4 x 100) + (5 x 10) + (9 x 1) + (8 x 0.1) + (4 x 0.01)

(9 x 10,000) + (4 x 1,000) + (3 x 100) + (2 x 10) + (4 x 1) + (2 x 0.1) + (5 x 0.01) =

(8 x 100,000) + (5 x 1,000) + (4 x 100) + (8 x 10) + (6 x 1) + (7 x 0.1) + (9 x 0.01) =

(4 x 1,000) + (6 x 100) + (8 x 10) + (2 x 1) + (8 x 0.1) + (6 x 0.01) =

(9 x 1,000,000) + (8 x 10,000) + (5 x 1,000) + (3 x 100) + (7 x 10) + (6 x 1) + (7 x 0.1) + (6 x 0.01)=

(5 x 10,000) + (4 x 1,000) + (9 x 100) + ( 3 x 10) + (7 x 1) + (3 x 0.1) + (2 x 0.01) =

(7 x 10,000) + (3 x 1,000) + (8 x 100) + (4 x 10) + (8 x 1) + (6 x 0.1) + (3 x 0.01) =