Solve Decimal Multiplication: 0.113 × 170 Step-by-Step

To solve this problem, we'll use straightforward multiplication while carefully considering the decimal place. Here are the steps we'll follow:

• Step 1: Treat $0.113$ as $113$ by ignoring the decimal point temporarily.

• Step 2: Multiply $113 \times 170$.

• Step 3: Reintroduce the decimal point in the product by placing it three decimal places from the right, as in $0.113$.

Let's work through each step:

Step 1: We rewrite $0.113$ as $113$.

Step 2: Multiplying $113$ by $170$ yields:

$\begin{aligned} 113 \times 170 &= 113 \times (100 + 70)\\ &= 113 \times 100 + 113 \times 70\\ &= 11300 + 7910\\ &= 19210 \end{aligned}$

Step 3: Now place the decimal point. Since the original number $0.113$ had three decimal places, the product $19210$ must be adjusted to three decimal places from the right, yielding:

$\begin{aligned} 19.210 \end{aligned}$

Thus, the final answer is:

$19.21$