Solve Decimal Multiplication: 0.1 × 0.35 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Convert the decimal numbers into a form that is easier to multiply.
• Step 2: Multiply the numbers as if they were whole numbers.
• Step 3: Adjust the product by placing the decimal point correctly.

Now, let's work through each step:

Step 1: Convert the decimals $0.1$ and $0.35$ into whole number expressions:

• $0.1$ can be thought of as $\frac{1}{10}$.
• $0.35$ can be thought of as $\frac{35}{100}$.

Step 2: Multiply as whole numbers: Multiply $1$ and $35$ to obtain $35$.

Step 3: Adjust the decimal point:

• $0.1$ has 1 decimal place.
• $0.35$ has 2 decimal places.

Thus, their product should have $1 + 2 = 3$ decimal places.

Therefore, the product of $0.1$ and $0.35$ is $0.035$.

Looking at the choices provided:

• Choice 1: $0.35$ is incorrect as it does not consider the decimal adjustment.
• Choice 2: $0.035$ is correct.
• Choice 3: $0.350$ is incorrect as it has an extra zero and maintains the incorrect placement of the decimal point.
• Choice 4: $0.310$ is incorrect as it does not correspond with the straightforward multiplication of the operands.

Thus, the correct choice is $0.035$.