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To convert the given values into standard form, we systematically go through each conversion, ensuring that all values are expressed in scientific notation. Here's the detailed step-by-step solution:
1. First Row Conversions:
- Given metres: [tex]\(2.3 \times 10^0 \, m\)[/tex]
- Centimetres:
[tex]\[ 2.3 \, m \times 100 = 230 \, cm = 2.3 \times 10^2 \, cm \][/tex]
- Millimetres:
[tex]\[ 2.3 \, m \times 1000 = 2300 \, mm = 2.3 \times 10^3 \, mm \][/tex]
- Micrometres:
[tex]\[ 2.3 \, m \times 1000000 = 2300000 \, \mu m = 2.3 \times 10^6 \, \mu m \][/tex]
2. Second Row Conversions:
- Given metres: [tex]\(4 \times 10^{-6} \, m\)[/tex]
- Centimetres:
[tex]\[ 4 \times 10^{-6} \, m \times 100 = 0.0004 \, cm = 4 \times 10^{-4} \, cm \][/tex]
- Millimetres:
[tex]\[ 4 \times 10^{-6} \, m \times 1000 = 0.004 \, mm = 4 \times 10^{-3} \, mm \][/tex]
- Micrometres:
[tex]\[ 4 \times 10^{-6} \, m \times 1000000 = 4 \, \mu m = 4 \times 10^0 \, \mu m \][/tex]
3. Third Row:
- Given micrometres: [tex]\(4 \times 10^1 \, \mu m\)[/tex]
4. Fourth Row:
- Given millimetres: [tex]\(1.2 \times 10^1 \, mm\)[/tex]
5. Fifth Row:
- Given centimetres: [tex]\(2.5 \times 10^0 \, cm\)[/tex]
After converting and organizing the values in standard form, the complete table is as follows:
\begin{tabular}{|c|c|c|c|}
\hline In metres [tex]$( m )$[/tex] & In centimetres [tex]$( cm )$[/tex] & In millimetres [tex]$( mm )$[/tex] & In Micrometres [tex]$(\mu m )$[/tex] \\
\hline [tex]$2.3 \times 10^0 \, m$[/tex] & [tex]$2.3 \times 10^2 \, cm$[/tex] & [tex]$2.3 \times 10^3 \, mm$[/tex] & [tex]$2.3 \times 10^6 \, \mu m$[/tex] \\
\hline [tex]$4 \times 10^{-6} \, m$[/tex] & [tex]$4 \times 10^{-4} \, cm$[/tex] & [tex]$4 \times 10^{-3} \, mm$[/tex] & [tex]$4 \times 10^0 \, \mu m$[/tex] \\
\hline & & & [tex]$4 \times 10^1 \, \mu m$[/tex] \\
\hline & & [tex]$1.2 \times 10^1 \, mm$[/tex] & \\
\hline & [tex]$2.5 \times 10^0 \, cm$[/tex] & & \\
\hline
\end{tabular}
1. First Row Conversions:
- Given metres: [tex]\(2.3 \times 10^0 \, m\)[/tex]
- Centimetres:
[tex]\[ 2.3 \, m \times 100 = 230 \, cm = 2.3 \times 10^2 \, cm \][/tex]
- Millimetres:
[tex]\[ 2.3 \, m \times 1000 = 2300 \, mm = 2.3 \times 10^3 \, mm \][/tex]
- Micrometres:
[tex]\[ 2.3 \, m \times 1000000 = 2300000 \, \mu m = 2.3 \times 10^6 \, \mu m \][/tex]
2. Second Row Conversions:
- Given metres: [tex]\(4 \times 10^{-6} \, m\)[/tex]
- Centimetres:
[tex]\[ 4 \times 10^{-6} \, m \times 100 = 0.0004 \, cm = 4 \times 10^{-4} \, cm \][/tex]
- Millimetres:
[tex]\[ 4 \times 10^{-6} \, m \times 1000 = 0.004 \, mm = 4 \times 10^{-3} \, mm \][/tex]
- Micrometres:
[tex]\[ 4 \times 10^{-6} \, m \times 1000000 = 4 \, \mu m = 4 \times 10^0 \, \mu m \][/tex]
3. Third Row:
- Given micrometres: [tex]\(4 \times 10^1 \, \mu m\)[/tex]
4. Fourth Row:
- Given millimetres: [tex]\(1.2 \times 10^1 \, mm\)[/tex]
5. Fifth Row:
- Given centimetres: [tex]\(2.5 \times 10^0 \, cm\)[/tex]
After converting and organizing the values in standard form, the complete table is as follows:
\begin{tabular}{|c|c|c|c|}
\hline In metres [tex]$( m )$[/tex] & In centimetres [tex]$( cm )$[/tex] & In millimetres [tex]$( mm )$[/tex] & In Micrometres [tex]$(\mu m )$[/tex] \\
\hline [tex]$2.3 \times 10^0 \, m$[/tex] & [tex]$2.3 \times 10^2 \, cm$[/tex] & [tex]$2.3 \times 10^3 \, mm$[/tex] & [tex]$2.3 \times 10^6 \, \mu m$[/tex] \\
\hline [tex]$4 \times 10^{-6} \, m$[/tex] & [tex]$4 \times 10^{-4} \, cm$[/tex] & [tex]$4 \times 10^{-3} \, mm$[/tex] & [tex]$4 \times 10^0 \, \mu m$[/tex] \\
\hline & & & [tex]$4 \times 10^1 \, \mu m$[/tex] \\
\hline & & [tex]$1.2 \times 10^1 \, mm$[/tex] & \\
\hline & [tex]$2.5 \times 10^0 \, cm$[/tex] & & \\
\hline
\end{tabular}
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