Let's go through each measurement and determine the number of significant digits in a detailed manner:
1. Measurement: [tex]$14000 \, \text{kg}$[/tex]
- To determine the number of significant digits, observe the specific digits that carry meaningful information about the precision of the measurement.
- The number 14000 has trailing zeros, but without additional context (like a decimal point or scientific notation), we do not treat these trailing zeros as significant.
- Thus, the significant digits are [tex]\(1\)[/tex] and [tex]\(4\)[/tex].
[tex]\[
\text{Significant digits: } 2
\][/tex]
2. Measurement: [tex]$0.006600 \, \text{J}$[/tex]
- Leading zeros are not significant as they only indicate the position of the decimal point.
- Here, the significant digits are [tex]\(6\)[/tex], [tex]\(6\)[/tex], [tex]\(0\)[/tex], and [tex]\(0\)[/tex].
[tex]\[
\text{Significant digits: } 4
\][/tex]
3. Measurement: [tex]$9.0 \times 10^{-1} \, \text{mL}$[/tex]
- In scientific notation, all the digits in the coefficient are considered significant.
- Here, the significant digits are [tex]\(9\)[/tex] and [tex]\(0\)[/tex].
[tex]\[
\text{Significant digits: } 2
\][/tex]
4. Measurement: [tex]$-4.0 \times 10^{-3} \, \text{kJ/mol}$[/tex]
- In scientific notation, the digits in the coefficient are always significant.
- Here, the significant digits are [tex]\(4\)[/tex] and [tex]\(0\)[/tex]. The negative sign does not affect the number of significant digits.
[tex]\[
\text{Significant digits: } 2
\][/tex]
Now, let's fill in the table with the number of significant digits for each measurement:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Measurement} & \text{Number of Significant Digits} \\
\hline
14000 \, \text{kg} & 2 \\
\hline
0.006600 \, \text{J} & 4 \\
\hline
9.0 \times 10^{-1} \, \text{mL} & 2 \\
\hline
-4.0 \times 10^{-3} \, \text{kJ/mol} & 2 \\
\hline
\end{tabular}
\][/tex]
