Sure, let's break down the process for solving this problem step by step.
### Step 1: Understanding the Values
We're given the expression to divide:
[tex]\[ 7.01 \times 10^7 \][/tex]
by
[tex]\[ 5.12 \times 10^5 \][/tex]
### Step 2: Perform the Division of the Coefficients
First, we divide the coefficients (the numbers in front of the exponential parts):
[tex]\[ \frac{7.01}{5.12} \approx 1.37 \][/tex]
### Step 3: Subtract the Exponents
Next, we'll handle the exponents:
[tex]\[ 10^7 \div 10^5 = 10^{7-5} = 10^2 \][/tex]
### Step 4: Combine the Results
Now, combine the results from the steps above:
[tex]\[ 1.37 \times 10^2 = 137 \][/tex]
### Step 5: Round to the Nearest Hundredth
In this case, 137 is already rounded to the nearest hundredth as it is a whole number without any decimal part needing rounding.
### Final Answer
The quotient when [tex]\( 7.01 \times 10^7 \)[/tex] is divided by [tex]\( 5.12 \times 10^5 \)[/tex] is:
[tex]\[ 137.00 \][/tex]
However, given that the problem asked for rounding to the nearest hundredth, and from the options:
The correct closest option is:
[tex]\[ 1.37 \times 10^2 \][/tex]
### Verification
We can verify that we have computed correctly by understanding that 137 is the same as [tex]\( 1.37 \times 10^2 \)[/tex]. Thus, the final selection fits perfectly the provided options, confirming that our result aligns exactly.
So, the correct choice is:
[tex]\[ \boxed{1.37 \times 10^2} \][/tex]
