Answer :
To solve the problem, we first determine how many sheets of copy paper, each with a thickness of [tex]$9.6 \times 10^{-8}$[/tex] kilometers, would be required to cover the distance to the Moon, which is approximately [tex]$3.84 \times 10^{5}$[/tex] kilometers.
Step 1: Write down the values
- Distance from Earth to the Moon:
[tex]$$ d = 3.84 \times 10^5 \text{ km} $$[/tex]
- Thickness of one piece of paper:
[tex]$$ t = 9.6 \times 10^{-8} \text{ km} $$[/tex]
Step 2: Set up the equation
We need to find the number of pieces, [tex]$N$[/tex], such that:
[tex]$$ N = \frac{d}{t} = \frac{3.84 \times 10^5}{9.6 \times 10^{-8}} $$[/tex]
Step 3: Divide the numbers
Perform the division by separating the numerical coefficients and the powers of 10:
1. Divide the coefficients:
[tex]$$ \frac{3.84}{9.6} = 0.4 $$[/tex]
2. Divide the powers of 10:
[tex]$$ \frac{10^5}{10^{-8}} = 10^{5 - (-8)} = 10^{13} $$[/tex]
Thus, the expression becomes:
[tex]$$ N = 0.4 \times 10^{13} $$[/tex]
Step 4: Express in standard scientific notation
Convert [tex]$0.4 \times 10^{13}$[/tex] to standard scientific notation:
[tex]$$ 0.4 \times 10^{13} = 4 \times 10^{12} $$[/tex]
Final Answer:
The number of pieces of copy paper required to reach from Earth to the Moon is:
[tex]$$ \boxed{4 \times 10^{12}} $$[/tex]
This corresponds to option A.
Step 1: Write down the values
- Distance from Earth to the Moon:
[tex]$$ d = 3.84 \times 10^5 \text{ km} $$[/tex]
- Thickness of one piece of paper:
[tex]$$ t = 9.6 \times 10^{-8} \text{ km} $$[/tex]
Step 2: Set up the equation
We need to find the number of pieces, [tex]$N$[/tex], such that:
[tex]$$ N = \frac{d}{t} = \frac{3.84 \times 10^5}{9.6 \times 10^{-8}} $$[/tex]
Step 3: Divide the numbers
Perform the division by separating the numerical coefficients and the powers of 10:
1. Divide the coefficients:
[tex]$$ \frac{3.84}{9.6} = 0.4 $$[/tex]
2. Divide the powers of 10:
[tex]$$ \frac{10^5}{10^{-8}} = 10^{5 - (-8)} = 10^{13} $$[/tex]
Thus, the expression becomes:
[tex]$$ N = 0.4 \times 10^{13} $$[/tex]
Step 4: Express in standard scientific notation
Convert [tex]$0.4 \times 10^{13}$[/tex] to standard scientific notation:
[tex]$$ 0.4 \times 10^{13} = 4 \times 10^{12} $$[/tex]
Final Answer:
The number of pieces of copy paper required to reach from Earth to the Moon is:
[tex]$$ \boxed{4 \times 10^{12}} $$[/tex]
This corresponds to option A.
