Multiply.
$\begin{array}{r}
0.347 \\
\times \quad 4.6 \\
\hline
\end{array}$
We need to find the product of two decimal numbers: \(0.347\) and \(4.6\). To perform this multiplication, we can use a method that involves treating the numbers as integers first and then adjusting the position of the decimal point based on the total number of decimal places in the original numbers. Both \(0.347\) and \(4.6\) are positive real numbers.
We ignore the decimal points and multiply the numbers as if they were integers: \(347\) and \(46\).
Calculating \(347 \times 46\):
\[347 \times 46 = 347 \times (40 + 6)\]
\[347 \times 40 = 13880\]
\[347 \times 6 = 2082\]
\[13880 + 2082 = 15962\]
The integer product is \(15962\).
The number \(0.347\) has \(3\) decimal places, and the number \(4.6\) has \(1\) decimal place. Therefore, the product must have a total of \(3 + 1 = 4\) decimal places. We take the integer product \(15962\) and place the decimal point so that there are \(4\) digits to its right. Starting from the right of \(15962\) and moving the decimal point \(4\) places to the left, we get \(1.5962\).
By combining the multiplication and the decimal point placement, we conclude that:
\[0.347 \times 4.6 = 1.5962\]
The final result is \(\boxed{1.5962}\).
In daily life, this calculation is useful when buying items by weight. For instance, if you purchase \(0.347\) kilograms of premium tea leaves at a price of \(\$4.60\) per kilogram, the total cost of your purchase would be \(0.347 \times 4.6 = 1.5962\), which rounds to \(\$1.60\). Understanding how to multiply decimals correctly is an essential skill for managing finances, measuring ingredients for cooking, or calculating physical quantities accurately.