Problem 64 - Algebra 1: Concepts and Skills

Question

Find the product. \(0.06 \times 0.0004\)

Step-by-Step Solution

Answer

The product of \(0.06 \times 0.0004\) is 0.000024.

Step 1: Write out the calculation

To start, write out the calculation that needs to be performed, which is \(0.06 \times 0.0004\).

Step 2: Multiply like integers

To simplify the calculation, ignore the decimal points and multiply these numbers as if they were whole numbers. So, think of it as multiplying 6 by 4, which gives you a product of 24.

Step 3: Count the number of decimal places

Next, count the total number of decimal places in the original numbers. There are two decimal places in 0.06, and four in 0.0004, so there are a total of six decimal places.

Step 4: Apply the decimal places to the answer

Now, apply these six decimal places to the answer from step 2. Starting from the rightmost digit of the answer and moving left, add a decimal point six places over to the left. This gives the final answer as 0.000024.

Key Concepts

Decimal Places

When working with decimals, understanding decimal places is essential. Decimal places refer to the digits to the right of a decimal point. For instance:

• The number 0.06 has two decimal places: the digits '0' and '6'.
• The number 0.0004 has four decimal places: the digits '0', '0', '0', and '4'.

Knowing the decimal places helps us deal with decimals in a variety of mathematical operations. For multiplication, this is crucial because it allows us to adjust the final answer accordingly. Counting decimal places is a key step to ensure the product is accurate. It ensures that our resultant number maintains the same level of precision as intended by the original decimal numbers.

Multiplication Steps

The multiplication of decimal numbers can initially be approached as if multiplying whole numbers. Here's how this is done:

• First, ignore the decimal points and multiply the numbers as if they were integers.
• In our example, treat 0.06 as 6 and 0.0004 as 4.
• Multiplying these gives us 24, just like a simple integer multiplication.

Approaching the multiplication this way simplifies the process greatly. It allows you to focus on the arithmetic before readdressing where the decimal should be placed. This step-by-step method ensures precision without overwhelming complications.

Product Calculation

After you multiply as if dealing with integers, the next step is to adjust the product by counting and applying decimal places. Here's what to do:

• Count all the decimal places from both original numbers. In our case, 0.06 has two, and 0.0004 has four, totaling six decimal places.
• Apply those decimal places to your product from the previous step.
• Insert a decimal into 24, making sure it has six places; hence, it becomes 0.000024.

Adapting the product this way ensures your answer correctly represents the precision inherent in the initial numbers. This approach might seem intricate, but with practice, it becomes instinctive and ensures accuracy in solving any multiplication of decimal problems.