To multiply the numbers 1.3 and 1.5, we can do the following calculation:
\[ 1.3 \times 1.5 \]
To make the calculation easier, let's first multiply them as whole numbers:
\[ 13 \times 15 \]
Calculating \(13 \times 15\):
\[ 13 \times 15 = 195 \]
Now, since we multiplied by whole numbers, we need to adjust for the decimal places. Both 1.3 and 1.5 have one decimal place each, so we need to move the decimal point two places to the left:
\[ 195 \rightarrow 1.95 \]
Thus,
\[ 1.3 \times 1.5 = 1.95 \]
Therefore, the result of the multiplication is:
\[ \boxed{1.95} \]