Sure! Let's perform the given mathematical operation step-by-step and report the answer in scientific notation to the correct number of significant figures.
The operation given is:
[tex]$
\frac{2.500 \times 10^2}{5.00 \times 10^{-5}}
$[/tex]
First, let's understand the operation.
1. We have a numerator [tex]\(2.500 \times 10^2\)[/tex] and a denominator [tex]\(5.00 \times 10^{-5}\)[/tex].
2. To divide these numbers, we first divide the coefficients and then divide the powers of 10 separately.
### Step 1: Divide the coefficients
The coefficient of the numerator is 2.500, and the coefficient of the denominator is 5.00.
We divide:
[tex]$
\frac{2.500}{5.00} = 0.500
$[/tex]
### Step 2: Divide the powers of 10
The power of 10 in the numerator is [tex]\(10^2\)[/tex], and the power of 10 in the denominator is [tex]\(10^{-5}\)[/tex].
When dividing powers of 10, we subtract the exponents:
[tex]$
10^2 \div 10^{-5} = 10^{2 - (-5)} = 10^{2 + 5} = 10^7
$[/tex]
### Step 3: Combine the results
Now, we combine the result of the coefficient division and the power of 10 division:
[tex]$
0.500 \times 10^7
$[/tex]
### Step 4: Express in scientific notation
To express the result in proper scientific notation, we adjust the coefficient to be between 1 and 10. Here, [tex]\(0.500 \times 10^7\)[/tex] can be written as [tex]\(5.0 \times 10^6\)[/tex], since:
[tex]$
0.500 \times 10^7 = 5.0 \times 10^6
$[/tex]
### Step 5: Use the correct number of significant figures
Both the numerator (2.500) and the denominator (5.00) have three significant figures. Thus, our final answer should also have three significant figures.
Therefore, the result is:
Coefficient
[tex]$
\boxed{5.0}
$[/tex]
Exponent
[tex]$
\boxed{6}
$[/tex]
