Decimal Multiplication Practice Problems & Solutions

Let's solve the problem of multiplying $0.1$ and $7.33$ step by step.

Step 1: Rewrite the two numbers without considering the decimal points. Calculate the product of 10 and 733.

Step 2: The result of $10 \times 733$ is $7330$.

Step 3: Count the total number of decimal places in the original factors $0.1$ and $7.33$.
- $0.1$ has 1 decimal place.
- $7.33$ has 2 decimal places.
Together, they amount to 3 decimal places.

Step 4: In the product $7330$, move the decimal point backwards to account for the 3 decimal places. So, the decimal point goes three places from the end of the number.

The result is $0.733$.

Therefore, $0.1 \times 7.33 = 0.733$.

The correct answer choice is $0.733$.

To multiply $0.1$ by $4.35$, move the decimal point in $4.35$ one place to the left. Thus, $0.1 \times 4.35 = 0.435$.

To multiply the decimal fractions $0.1$ and $0.008$, first, ignore the decimal points and multiply the numbers as if they were whole numbers:

$1 \times 8 = 8$

Now, count the total number of decimal places in both of the original numbers. Here, $0.1$ has 1 decimal place, and $0.008$ has 3 decimal places, so there are 4 decimal places in total.

Thus, in the product, place the decimal point so that there are 4 digits to the right of the decimal point:

$0.0008$

To solve $0.1 \times 0.999$, we need to follow these steps carefully:

• Step 1: Treat the numbers as integers and multiply them. Ignoring the decimal points temporarily, multiply $1$ by $999$:
  $\quad 1 \times 999 = 999$.
• Step 2: Determine the total number of decimal places in the factors.
  $\quad 0.1$ has 1 decimal place.
  $\quad 0.999$ has 3 decimal places.
  Therefore, the product should have $1 + 3 = 4$ decimal places.
• Step 3: Position the decimal in the product calculated in step 1.
  $\quad 999$ with 4 decimal places becomes $0.0999$.

Therefore, the product of $0.1 \times 0.999$ is $0.0999$.

To solve the problem of finding $0.1 \times 33.4$, we'll employ the following method:

• Step 1: Multiply the numbers without considering decimals.
  Calculate $1 \times 33.4 = 33.4$.
• Step 2: Determine the decimal placement.
  The number $0.1$ has one decimal place, and $33.4$ has one decimal place. Therefore, the product should have $1 + 1 = 2$ decimal places.
• Step 3: Apply the decimal adjustment.
  Take the product $33.4$ and insert two decimal places from the right. This results in $3.34$.

Thus, the solution to the problem $0.1 \times 33.4$ is $\mathbf{3.34}$.