Multiply the numbers: Multiply the two given numbers.To multiply 2.13 by 0.197, align the decimal points and multiply as if they were whole numbers.Calculation: 2.13×0.197\begin{align*}
&2.13 \
&\times 0.197 \
&\underline{\phantom{0}------} \
&\phantom{0}1491 &\text{(This is inline_latex_0 multiplied by inline_latex_4, with three decimal places to the right)} \
&\phantom{0000} &\text{(This is inline_latex_0 multiplied by inline_latex_6, with two decimal places to the right; however, since inline_latex_6 is zero, the result is inline_latex_8)} \
&426 &\text{(This is inline_latex_0 multiplied by inline_latex_10, with one decimal place to the right)} \
&\underline{\phantom{0}------} \
&\phantom{0}41941 &\text{(Sum of the above products, before adjusting the decimal place)}
\end{align*}Now, count the total number of decimal places in the original numbers (0.1971 in 2.13 and 0.1973 in 0.197), which is 0.1975.Place the decimal point in the result to have 0.1975 decimal places from the right.Final result: 0.1977
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