Sure, let's convert the given decimals to fractions with the specified bases. We will detail each step for better understanding.
1. Decimal 0.4:
- [tex]\(0.4 \times 10 = 4.0\)[/tex]
- [tex]\(0.4 \times 1000 = 400.0\)[/tex]
- [tex]\(0.4 \times 10,000 = 4,000.0\)[/tex]
- [tex]\(0.4 \times 100,000 = 40,000.0\)[/tex]
2. Decimal 0.375:
- [tex]\(0.375 \times 10 = 3.75\)[/tex]
- [tex]\(0.375 \times 1000 = 375.0\)[/tex]
- [tex]\(0.375 \times 10,000 = 3,750.0\)[/tex]
- [tex]\(0.375 \times 100,000 = 37,500.0\)[/tex]
3. Decimal 0.04:
- [tex]\(0.04 \times 10 = 0.4\)[/tex]
- [tex]\(0.04 \times 1000 = 40.0\)[/tex]
- [tex]\(0.04 \times 10,000 = 400.0\)[/tex]
- [tex]\(0.04 \times 100,000 = 4,000.0\)[/tex]
4. Decimal 0.0000156:
- [tex]\(0.0000156 \times 10 = 0.000156\)[/tex]
- [tex]\(0.0000156 \times 1000 = 0.0156\)[/tex]
- [tex]\(0.0000156 \times 10,000 = 0.156\)[/tex]
- [tex]\(0.0000156 \times 100,000 = 1.56\)[/tex]
Here is the completed table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Decimal & 10 & 1000 & 10,000 & 100,000 \\
\hline
0.4 & 4.0 & 400.0 & 4000.0 & 40000.0 \\
\hline
0.375 & 3.75 & 375.0 & 3750.0 & 37500.0 \\
\hline
0.04 & 0.4 & 40.0 & 400.0 & 4000.0 \\
\hline
0.0000156 & 0.000156 & 0.0156 & 0.156 & 1.56 \\
\hline
\end{tabular}
\][/tex]
This table represents the conversion of each decimal to its respective fraction based on the given bases.
