Math Snap

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, $.9 \times10^{-2} \mathrm{~m}$. This is written in scientific notation, so all the digits in the coefficient are significant.
$$\text{Number of significant digits in }.9 \times10^{-2} \mathrm{~m} =2$$

STEP 3

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

STEP 4

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

Finally, let's consider the fourth measurement, $-2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol}$. This is written in scientific notation, so all the digits in the coefficient are significant.
$$\text{Number of significant digits in } -2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol} =2$$So, the number of significant digits in each measurement is as follows\begin{tabular}{|c|c|} \hline measurement & $\begin{array}{c}\text { number of } \\ \text { significant } \\ \text { digits }\end{array}$ \\
\hline $3.9 \times10^{-2} \mathrm{~m}$ & $2$ \\
\hline $0.006700 \mathrm{~J}$ & $4$ \\
\hline $87700 . \mathrm{~kg}$ & $3$ \\
\hline$-2.0 \times10^{-2} \mathrm{~kJ} / \mathrm{mol}$ & $2$ \\
\hline\end{tabular}