Certainly! Let's solve the given problem step by step.
### Step 1: Understanding the problem
We have been given:
[tex]\[
\frac{0.863 \times 23}{2589}
\][/tex]
### Step 2: Performing the multiplication
First, we need to multiply the decimal number [tex]\(0.863\)[/tex] by [tex]\(23\)[/tex].
[tex]\[
0.863 \times 23
\][/tex]
The result of this multiplication is:
[tex]\[
19.849
\][/tex]
### Step 3: Setting up the fraction
Now, we place the result of the multiplication over the denominator given in the problem.
[tex]\[
\frac{19.849}{2589}
\][/tex]
### Step 4: Performing the division
Next, we divide the numerator [tex]\(19.849\)[/tex] by the denominator [tex]\(2589\)[/tex].
[tex]\[
19.849 \div 2589
\][/tex]
The result of this division is:
[tex]\[
0.007666666666666667
\][/tex]
### Step 5: Conclusion
So, when you simplify the expression [tex]\(\frac{0.863 \times 23}{2589}\)[/tex], you get approximately:
[tex]\[
0.007666666666666667
\][/tex]
### Summary
The steps we followed were:
1. Multiply [tex]\(0.863\)[/tex] by [tex]\(23\)[/tex] to get [tex]\(19.849\)[/tex].
2. Set up the fraction [tex]\(\frac{19.849}{2589}\)[/tex].
3. Divide [tex]\(19.849\)[/tex] by [tex]\(2589\)[/tex] to get approximately [tex]\(0.007666666666666667\)[/tex].
Thus, the simplified result of the given expression is [tex]\(0.007666666666666667\)[/tex].
