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QuestionCount the significant digits in these measurements: 3.9×10−2 mL3.9 \times 10^{-2} \mathrm{~mL}, 0.006700 J0.006700 \mathrm{~J}, 87700 kg87700 \mathrm{~kg}, −2.0×10−2 kJ/mol-2.0 \times 10^{-2} \mathrm{~kJ/mol}.

Studdy Solution

STEP 1

Assumptions1. Significant digits include all the digits from the first non-zero digit to the last non-zero digit in the decimal part, including any zeros that are between these digits. . In scientific notation, all the digits in the coefficient are significant.
3. Leading zeros are not significant.
4. Trailing zeros are significant if they are after a decimal point.
5. Trailing zeros in a whole number with no written decimal point are not significant.

STEP 2

Let's start with the first measurement, .9×10−2 m.9 \times10^{-2} \mathrm{~m}. This is written in scientific notation, so all the digits in the coefficient are significant.
Number of significant digits in .9×10−2 m=2\text{Number of significant digits in }.9 \times10^{-2} \mathrm{~m} =2

STEP 3

Next, let's consider the second measurement, 0.006700 J0.006700 \mathrm{~J}. The leading zeros are not significant, but the trailing zeros after the decimal point are significant.
Number of significant digits in 0.006700 J=\text{Number of significant digits in }0.006700 \mathrm{~J} =

STEP 4

Now, let's consider the third measurement, 87700. kg87700 . \mathrm{~kg}. This is a whole number with no written decimal point, so the trailing zeros are not significant.
Number of significant digits in 87700. kg=3\text{Number of significant digits in }87700 . \mathrm{~kg} =3

STEP 5

Finally, let's consider the fourth measurement, −2.0×10−2 kJ/mol-2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol}. This is written in scientific notation, so all the digits in the coefficient are significant.
Number of significant digits in −2.0×10−2 kJ/mol=2\text{Number of significant digits in } -2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol} =2So, the number of significant digits in each measurement is as follows\begin{tabular}{|c|c|} \hline measurement &  number of  significant  digits \begin{array}{c}\text { number of } \\ \text { significant } \\ \text { digits }\end{array} \\ \hline 3.9×10−2 m3.9 \times10^{-2} \mathrm{~m} & 22 \\ \hline 0.006700 J0.006700 \mathrm{~J} & 44 \\ \hline 87700. kg87700 . \mathrm{~kg} & 33 \\ \hline−2.0×10−2 kJ/mol-2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol} & 22 \\ \hline\end{tabular}

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