All Operations in Decimal Fractions: Multiplication by 100

To solve this problem, we'll focus on the rule for multiplying decimal fractions by powers of 10:

• Move the decimal point to the right for each power of ten involved in the multiplication.

• For $100$, we move the decimal point two places to the right.

Let's apply this to our problem:

The given number is $0.314$.

Step 1: Identify the number of decimal places in $0.314$, which is 3 digits long: "314".

Step 2: Multiplying $0.314$ by $100$ requires us to move the decimal point two places to the right.

Before moving the decimal point:

$0.314$

Move the decimal point two places right:

$3.14$

Effectively, the number becomes $31.4$.

Hence, the result of $0.314 \times 100 = 31.4$.

Therefore, the solution to the problem is $31.4$.

The correct answer choice from the options is:

$31.4$

To solve the problem of finding $11.41 \times 100$, we'll follow these steps:

• Step 1: Understand the operation needed - multiplying by 100 involves moving the decimal point two places to the right.
• Step 2: Identify the initial position of the decimal point in the number 11.41. Initially, it is between 11 and 41.
• Step 3: Move the decimal two places to the right. This results in the number shifting from 11.41 to 1141.0.
• Step 4: Simplify by removing the unnecessary decimal zero, resulting in the final value of 1141.

Therefore, the solution to the problem $11.41 \times 100$ is $1141$.

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

• Step 1: Identify the original position of the decimal point in 3.412.
• Step 2: Shift the decimal point two places to the right because we are multiplying by 100.
• Step 3: Write down the new number after shifting the decimal point.

Now, let's perform the solution:
Step 1: In the number 3.412, the decimal point is initially between the 3 and the 4.
Step 2: We shift this decimal point two places to the right, which changes the value to 341.2.
Step 3: The resulting number after this operation is 341.2.

Therefore, the solution to the problem is $341.2$.