Let's analyze each measurement step by step to determine the number of significant digits.
1. Measurement: 0.008900 J
To find the number of significant figures, we need to count all digits starting from the first non-zero digit:
- 0.008900
- The first non-zero digit is 8.
- Digits: 8, 9, 0, 0.
Therefore, 0.008900 J has 4 significant digits.
2. Measurement: 37100 kg
Here, we need to consider the rules for zeros in different positions:
- 37100
- Digits: 3, 7, 1, 0, 0.
Since trailing zeros in a whole number without a decimal point are not considered significant:
- 37100 has 3 significant digits (3, 7, 1).
3. Measurement: [tex]\(4.7 \times 10^{-2}\)[/tex] mL
Scientific notation makes it clearer:
- [tex]\(4.7 \times 10^{-2}\)[/tex]
- Digits: 4, 7.
Therefore, [tex]\(4.7 \times 10^{-2}\)[/tex] mL has 2 significant digits.
4. Measurement: [tex]\(-3.0 \times 10^{-2}\)[/tex] kJ/mol
Similarly, in scientific notation:
- [tex]\(-3.0 \times 10^{-2}\)[/tex]
- Digits: 3, 0.
Since the trailing zero after the decimal point is significant:
- [tex]\(-3.0 \times 10^{-2}\)[/tex] kJ/mol has 2 significant digits.
Summarizing all the results, we fill out the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
measurement & \begin{tabular}{c}
number of \\
significant \\
digits
\end{tabular} \\
\hline 0.008900 J & 4 \\
\hline 37100 kg & 3 \\
\hline $4.7 \times 10^{-2}$ mL & 2 \\
\hline $-3.0 \times 10^{-2}$ kJ/mol & 2 \\
\hline
\end{tabular}
\][/tex]
