Problem 262 - Intermediate Algebra

Question

In the following exercises, multiply. $$ (0.08)(52.45) $$

Step-by-Step Solution

Answer

4.196

Step 1: Setup the multiplication

Write down the numbers vertically as you would for a standard multiplication, aligning the decimal points for clarity.

Step 2: Remove the decimal points

Temporarily ignore the decimal points and multiply 8 by 5245. This simplifies the calculation process. So you multiply 8 by 5245.

Step 3: Perform the multiplication

Multiply 8 by 5245 to get 41960.

Step 4: Reintroduce the decimal points

Count the total number of decimal places in the original numbers. 0.08 has 2 decimal places and 52.45 has 2 decimal places, making a total of 4 decimal places.

Step 5: Apply the decimal points

Starting from the right, place the decimal point 4 places to the left in 41960. This gives the final result of 4.1960, which can be simplified to 4.196.

Key Concepts

decimal points in multiplication

Understanding how to handle decimal points in multiplication is key to solving problems accurately. When multiplying numbers with decimals, it's important to note where the decimal points are initially located.

• If you multiply a number with two decimal places by another number with two decimal places, the total number of decimal places in the answer will be the sum of the decimal places in both numbers.
• In the given exercise, 0.08 has 2 decimal places, and 52.45 has 2 decimal places. Thus, their product will have 4 decimal places in total.

Grasping this concept helps in ensuring that you place the decimal correctly in the final answer. Misplacing the decimal point can lead to incorrect results, which is why careful counting and placing are essential.

step-by-step multiplication

Working through multiplication problems step-by-step helps maintain accuracy and clarity.
Follow these steps closely for multiplying decimals:

• Step 1: Write down the numbers vertically, aligning the decimal points to help visualize the multiplication.
• Step 2: Remove the decimal points temporarily. This simplifies the process by converting it into regular multiplication.
• Step 3: Multiply the numbers as if they were whole numbers. For instance, multiply 8 by 5245 to get 41960.
• Step 4: Count the decimal places in the original numbers. Here, both 0.08 and 52.45 have 2 decimal places each.
• Step 5: Place the decimal point in the result. Since there are 4 decimal places in total, place the decimal point 4 places from the right in the number 41960, resulting in 4.1960. Simplify if necessary; in this case, the final answer is 4.196.

Always follow each step carefully to minimize mistakes.

placing decimal points

Placing decimal points correctly is extremely important in multiplication. Here’s a detailed explanation:
After multiplying the numbers as if they were whole, you need to count the total decimal places from the factors.

• In our example, the number 0.08 has 2 decimal places, and 52.45 also has 2 decimal places. This makes a total of 4 decimal places.
• Once you have the product, which is 41960 from multiplying 8 and 5245, you need to reintroduce the decimal point.
• Starting from the right end of the product, count 4 places to the left and place the decimal point there. For 41960, it becomes 4.1960.
• You can further simplify this by removing the trailing zero, resulting in 4.196.

By meticulously following these steps, you ensure that the decimal point is accurately placed, leading to the correct answer.