Answer :
Sure, let's tackle this problem step by step.
### Question 11: Height of a Stack of Paper
#### Given Information:
- Thickness of one piece of paper: \(0.004\) inches
- Number of pieces of paper: \(1{,}000{,}000\)
#### Goal:
Calculate the height of a stack of \(1{,}000{,}000\) pieces of paper and express the height in scientific notation.
### Step-by-Step Solution:
1. Identify the Thickness of One Piece of Paper:
The thickness of one piece of paper is \(0.004\) inches.
2. Identify the Number of Pieces of Paper:
The number of pieces of paper in the stack is \(1{,}000{,}000\).
3. Calculate the Total Height of the Stack:
To find the total height of the stack, you multiply the thickness of one piece of paper by the number of pieces of paper.
Total height = Thickness of one piece of paper \(\times\) Number of pieces of paper
[tex]\[ \text{Total height} = 0.004 \, \text{inches} \times 1{,}000{,}000 \][/tex]
4. Perform the Multiplication:
[tex]\[ \text{Total height} = 0.004 \times 1{,}000{,}000 \][/tex]
[tex]\[ \text{Total height} = 4{,}000 \, \text{inches} \][/tex]
5. Express the Total Height in Scientific Notation:
Scientific notation expresses a number as a product of a coefficient (a number between 1 and 10) and a power of 10.
The total height of \(4{,}000\) inches can be written as:
[tex]\[ 4{,}000 = 4.00 \times 10^3 \][/tex]
In scientific notation, the height of the stack is \(4.00 \times 10^3\) inches.
### Final Answer:
The height of a stack of [tex]\(1{,}000{,}000\)[/tex] pieces of paper, each [tex]\(0.004\)[/tex] inch thick, is [tex]\(4{,}000\)[/tex] inches, which can be expressed in scientific notation as [tex]\(4.00 \times 10^3\)[/tex] inches.
### Question 11: Height of a Stack of Paper
#### Given Information:
- Thickness of one piece of paper: \(0.004\) inches
- Number of pieces of paper: \(1{,}000{,}000\)
#### Goal:
Calculate the height of a stack of \(1{,}000{,}000\) pieces of paper and express the height in scientific notation.
### Step-by-Step Solution:
1. Identify the Thickness of One Piece of Paper:
The thickness of one piece of paper is \(0.004\) inches.
2. Identify the Number of Pieces of Paper:
The number of pieces of paper in the stack is \(1{,}000{,}000\).
3. Calculate the Total Height of the Stack:
To find the total height of the stack, you multiply the thickness of one piece of paper by the number of pieces of paper.
Total height = Thickness of one piece of paper \(\times\) Number of pieces of paper
[tex]\[ \text{Total height} = 0.004 \, \text{inches} \times 1{,}000{,}000 \][/tex]
4. Perform the Multiplication:
[tex]\[ \text{Total height} = 0.004 \times 1{,}000{,}000 \][/tex]
[tex]\[ \text{Total height} = 4{,}000 \, \text{inches} \][/tex]
5. Express the Total Height in Scientific Notation:
Scientific notation expresses a number as a product of a coefficient (a number between 1 and 10) and a power of 10.
The total height of \(4{,}000\) inches can be written as:
[tex]\[ 4{,}000 = 4.00 \times 10^3 \][/tex]
In scientific notation, the height of the stack is \(4.00 \times 10^3\) inches.
### Final Answer:
The height of a stack of [tex]\(1{,}000{,}000\)[/tex] pieces of paper, each [tex]\(0.004\)[/tex] inch thick, is [tex]\(4{,}000\)[/tex] inches, which can be expressed in scientific notation as [tex]\(4.00 \times 10^3\)[/tex] inches.
