Sure, I will provide a detailed, step-by-step solution for determining the number of significant digits for each of the given measurements.
### Measurement: [tex]$35500 . kg$[/tex]
1. Step 1: Analyze the given number for significant digits.
2. Step 2: Note that the number ends with a decimal point, which indicates that the trailing zeros are significant.
3. Step 3: Count all digits from the left to the right: 3, 5, 5, 0, 0.
Thus, the total number of significant digits is 3.
### Measurement: 0.001000 J
1. Step 1: Analyze the given number for significant digits.
2. Step 2: Note that the leading zeros are not significant as they only indicate the position of the decimal point.
3. Step 3: Count the digits from the first non-zero digit (1 onwards): 1, 0, 0, 0.
Thus, the total number of significant digits is 4.
### Measurement: [tex]$-8.0 \times 10^{-3} kJ / mol$[/tex]
1. Step 1: Analyze the given number for significant digits.
2. Step 2: Only the digits in the coefficient (i.e., -8.0) count towards significant digits. Ignore the exponential part (i.e., [tex]$10^{-3}$[/tex]) as it does not affect the number of significant digits.
3. Step 3: For -8.0, the digits 8 and the trailing zero after the decimal point are significant.
Thus, the total number of significant digits is 2.
So, the completed table with the number of significant digits for each measurement is as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
measurement & \begin{tabular}{c}
number of \\
significant \\
digits
\end{tabular} \\
\hline
$35500 . kg$ & 3 \\
\hline
0.001000 J & 4 \\
\hline
$-8.0 \times 10^{-3} kJ / mol$ & 2 \\
\hline
\end{tabular}
\][/tex]
