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## Spectrum Math Grade 5 Chapter 2 Lesson 2.5 Expanded Form with Whole Numbers Answers Key

Expanded form is a way to write a number that shows the sum of values of each digit of a number. To use expanded form, a number has to be separated into each of its parts using place value.

5,423 = 5,000 + 400 + 20 + 3

39,572 = 30,000 + 9,000 + 500 + 70 + 2

**Write each number in Expanded form.**

Question 1.

a. 430

_______

Answer:

400 + 30

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

430 = 400 + 30

4 in hundreds places is written as 4 x 100 = 400.

3 in tens place is written as 3 x 10 = 30.

So, the sum of 400 + 30 = 430.

b. 721

_______

Answer:

700 + 20 + 1

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

721 = 700 + 20 + 1

7 in hundreds places is written as 7 x 100 = 700.

2 in tens place is written as 2 x 10 = 20.

1 in ones place is written as 1 x 1 = 1.

So, the sum of 700 + 20 + 1 = 721.

Question 2.

a. 3,465

_______

Answer:

3,000 + 400 + 60 + 5

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

3,465 = 3,000 + 400 + 60 + 5

3 in thousands place is written as 3 x 1000 = 3000

4 in hundreds places is written as 4 x 100 = 400.

6 in tens place is written as 6 x 10 = 60.

5 in ones place is written as 5 x 1 = 5.

So, the sum of 3,000 + 400 + 60 + 5 = 3465.

b. 43,645

_______

Answer:

40,000 + 3,000 + 600 + 40 + 5

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

43,645 = 40,000 + 3,000 + 600 + 40 + 5

4 in ten thousands place is written as 4 x 10,000 = 40,000

3 in thousands place is written as 3 x 1000 = 3000

6 in hundreds places is written as 6 x 100 = 600.

4 in tens place is written as 4 x 10 = 40.

5 in ones place is written as 5 x 1 = 5.

So, the sum of 40,000 + 3,000 + 600 + 40 + 5 = 43,645

Question 3.

a. 90,327

_______

Answer:

90,000 + 300 + 20 + 7

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

90,327 = 90,000 + 300 + 20 + 7

9 in ten thousands place is written as 9 x 10,000 = 90,000

3 in hundreds places is written as 3 x 100 = 300.

2 in tens place is written as 2 x 10 = 20.

7 in ones place is written as 7 x 1 = 7.

So, the sum of 90,000 + 300 + 20 + 7 = 90,327

b. 4,009

_______

Answer:

4,000 + 9

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

4,009 = 4,000 + 9

4 in thousands place is written as 4 x 1000 = 4000

9 in ones place is written as 9 x 1 = 9.

So, the sum of 4,000 + 9 = 4,009

Question 4.

a. 653,410

_______

Answer:

600,000 + 50,000 + 3,000 + 400 + 10

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

653,410 = 600,000 + 50,000 + 3,000 + 400 + 10

6 in hundred thousands place is written as 6 x 100,000 = 600,000

5 in ten thousands place is written as 5 x 10,000 = 50,000

3 in thousands place is written as 3 x 1000 = 3000

4 in hundreds places is written as 4 x 100 = 400.

1 in tens place is written as 1 x 10 = 10.

So, the sum of 600,000 + 50,000 + 3,000 + 400 + 10 = 653,410

b. 103,254

_______

Answer:

100,000 + 3,000 + 200 + 50 + 4

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

103,254 = 100,000 + 3,000 + 200 + 50 + 4

1 in hundred thousands place is written as 6 x 100,000 = 100,000

3 in thousands place is written as 3 x 1000 = 3000

2 in hundreds places is written as 2 x 100 = 200

5 in tens place is written as 5 x 10 = 50

4 in ones place is written as 4 x 1 = 4

So, the sum of 100,000 + 3,000 + 200 + 50 + 4 = 103,254

Question 5.

a. 199,482

_______

Answer:

100,000 + 90,000 + 9,000 + 400 + 80 + 2

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

199,482 = 100,000 + 90,000 + 9,000 + 400 + 80 + 2

1 in hundred thousands place is written as 1 x 100,000 = 100,000

9 in ten thousands place is written as 9 x 10,000 = 90,000

9 in thousands place is written as 9 x 1000 = 9000

4 in hundreds places is written as 4 x 100 = 400.

8 in tens place is written as 8 x 10 = 80.

2 in ones place is written as 2 x 1 = 2

So, the sum of 100,000 + 90,000 + 9,000 + 400 + 80 + 2 = 199,482

b. 32,451

_______

Answer:

30,000 + 2,000 + 400 + 50 + 1

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

32,451 = 30,000 + 2,000 + 400 + 50 + 1

3 in ten thousands place is written as 3 x 10,000 = 30,000

2 in thousands place is written as 2 x 1000 = 2000

4 in hundreds places is written as 4 x 100 = 400.

5 in tens place is written as 5 x 10 = 50.

1 in ones place is written as 1 x 1 = 1

So, the sum of 30,000 + 2,000 + 400 + 50 + 1 = 32,451

Question 6.

a. 9,342,751

_______

Answer:

9,000,000 + 300,000 + 40,000 + 2,000 + 700 + 50 + 1

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

9,342,751 = 9,000,000 + 300,000 + 40,000 + 2,000 + 700 + 50 + 1

9 in millions place is written as 9 x 1,000,000 = 9,000,000

3 in hundred thousands place is written as 3 x 100,000 = 300,000

4 in ten thousands place is written as 4 x 10,000 = 40,000

2 in thousands place is written as 2 x 1000 = 2000

7 in hundreds places is written as 7 x 100 = 700.

5 in tens place is written as 5 x 10 = 50.

1 in ones place is written as 1 x 1 = 1

So, the sum of 9,000,000 + 300,000 + 40,000 + 2,000 + 700 + 50 + 1 = 9,342,751

b. 2,500,055

_______

Answer:

2,000,000 + 500,000 + 50 + 5

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

2,500,055 = 2,000,000 + 500,000 + 50 + 5

2 in millions place is written as 2 x 1,000,000 = 2,000,000

5 in hundred thousands place is written as 5 x 100,000 = 500,000

5 in tens place is written as 5 x 10 = 50

5 in ones place is written as 5 x 1 = 5

So, the sum of 2,000,000 + 500,000 + 50 + 5 = 2,500,055

Question 7.

a. 598,721

_______

Answer:

500,000 + 90,000 + 8,000 + 700 + 20 + 1

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

598,721 = 500,000 + 90,000 + 8,000 + 700 + 20 + 1

5 in hundred thousands place is written as 5 x 100,000 = 500,000

9 in ten thousands place is written as 9 x 10, 000 = 90,000

8 in thousands place is written as 8 x 1000 = 8000

7 in hundreds places is written as 7 x 100 = 700

2 in tens place is written as 2 x 10 = 20

1 in ones place is written as 1 x 1 = 1

So, the sum of 500,000 + 90,000 + 8,000 + 700 + 20 + 1 = 598,721

b. 69,003

_______

Answer:

60,000 + 9,000 + 3

Explanation:

We know that,

Expanded form is a method to show the sum of values of each digit of a number.

In expanded form we separate a number into each of its parts using place value.

Given,

69,003 = 60,000 + 9,000 + 3

6 in ten thousands place is written as 6 x 10,000 = 60,000

9 in thousands place is written as 9 x 1000 = 9,000

3 in ones place is written as 3 x 1 = 3

So, the sum of 60,000 + 9,000 + 3 = 69,003