Sure, let's solve this step-by-step.
1. Convert the mixed fraction to an improper fraction:
The mixed fraction is [tex]\(-3 \frac{6}{7}\)[/tex].
To convert [tex]\(-3 \frac{6}{7}\)[/tex] into an improper fraction, we first express [tex]\(3\)[/tex] as [tex]\( \frac{3 \cdot 7}{7} = \frac{21}{7}\)[/tex].
So, [tex]\(-3 \frac{6}{7} = - \left( \frac{21}{7} + \frac{6}{7} \right) = - \frac{27}{7}\)[/tex].
Now, express [tex]\( - \frac{27}{7} \)[/tex] as a decimal:
[tex]\(- \frac{27}{7} = -3.857142857142857\)[/tex].
2. Convert the fraction [tex]\(\frac{1}{81}\)[/tex] to a decimal:
[tex]\(\frac{1}{81}\)[/tex] as a decimal is [tex]\(0.012345679012345678\)[/tex].
3. Use the given decimals directly:
The decimal numbers [tex]\(2.3\)[/tex] and [tex]\(-0.5\)[/tex] do not require conversion as they are already in decimal form.
4. Multiply all the numbers together:
Combine the values from the steps:
[tex]\[
(-3.857142857142857) \times 0.012345679012345678 \times 2.3 \times (-0.5).
\][/tex]
5. Calculate the result of the multiplication:
Multiplication of these four decimals gives:
[tex]\[
0.054761904761904755
\][/tex]
Therefore,
[tex]\[
\left(-3 \frac{6}{7}\right) \left(\frac{1}{81}\right) (2.3)(-0.5) = 0.054761904761904755.
\][/tex]
This is the detailed step-by-step solution for the given question.
