Questions: Count the significant digits in each of these measurements: measurement number of significant digits ------ 3.2 × 10^-2 mL □ -6.0 × 10^-3 kJ / mol □ 43600 kg □

Transcript text: Count the significant digits in each of these measurements: \begin{tabular}{|c|c|} \hline measurement & \begin{tabular}{c} number of \\ significant \\ digits \end{tabular} \\ \hline $3.2 \times 10^{-2} \mathrm{~mL}$ & $\square$ \\ \hline$-6.0 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol}$ & $\square$ \\ \hline 43600 kg & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Analyze the First Measurement

The first measurement is $3.2 \times 10^{-2} \, \text{mL}$. In scientific notation, the significant digits are the non-zero digits in the coefficient. Here, the coefficient is $3.2$, which has two significant digits.

Step 2: Analyze the Second Measurement

The second measurement is $-6.0 \times 10^{-3} \, \text{kJ/mol}$. Again, in scientific notation, the significant digits are the non-zero digits in the coefficient. The coefficient is $-6.0$, which has two significant digits because the trailing zero is significant.

Step 3: Analyze the Third Measurement

The third measurement is $43600 \, \text{kg}$. In this case, the number of significant digits depends on whether the trailing zeros are considered significant. Without additional context (such as a decimal point or scientific notation), we assume the trailing zeros are not significant. Therefore, the number of significant digits is three.

Final Answer

\[ \begin{array}{|c|c|} \hline \text{measurement} & \text{number of significant digits} \\ \hline 3.2 \times 10^{-2} \, \text{mL} & \boxed{2} \\ \hline -6.0 \times 10^{-3} \, \text{kJ/mol} & \boxed{2} \\ \hline 43600 \, \text{kg} & \boxed{3} \\ \hline \end{array} \]

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