Problem 63 - Algebra 1: Concepts and Skills

Question

Find the product. \(0.09 \times 0.02\)

Step-by-Step Solution

Answer

The result of the multiplication \(0.09 \times 0.02\) is \(0.0018\)

Step 1: Arrange the Numbers

First arrange the numbers in order for the multiplication. Here it would be \n\(0.09 \times 0.02\).

Step 2: Ignore the Decimal Points and Multiply

Next, remove the decimal points and multiply as if they are whole numbers. \nSo, it would look like \(9 \times 2 = 18\)

Step 3: Count the Decimal Places

Count the total number of decimal places in the multiplication. Here, there are two decimal places in 0.09 and two in 0.02. So, the total is four.

Step 4: Place the Decimal in the Product

Finally, place the decimal point in the product from Step 2 such that there are four numbers after it, counting from the right. As there are less than four digits, pad with zeroes. The final product is \(0.0018\)

Key Concepts

Decimal Places

Decimal places are crucial when working with decimals in multiplication. They refer to the number of digits found to the right of the decimal point.
For instance, in the number 0.09, there are two decimal places, as there are two digits (0 and 9) following the decimal.
To determine the total number of decimal places involved in a multiplication problem, you sum the decimals present in both numbers.
So, in the multiplication of 0.09 and 0.02, the total is four decimal places: two from each number.
This step is essential because it informs where the final decimal point should be placed in the product.

Arranging Numbers for Multiplication

Arranging numbers properly is the starting point of any multiplication exercise.
It means setting the numbers in the proper sequence—usually one above the other—before you start calculating.
In our example, you would set 0.09 directly above 0.02.
This step helps you to align the digits neatly, simplifying the calculation process, especially if you're working by hand.
Proper arrangement is key to avoiding errors, ensuring each digit is multiplied correctly.

Ignoring Decimal Points in Multiplication

When multiplying decimals, a helpful approach is to ignore the decimal points at the start.
This means initially treating the numbers like whole numbers.
For instance, in 0.09 and 0.02, ignore the decimals and multiply 9 by 2, which gives us 18.
This method simplifies the calculation, reducing potential mistakes from juggling decimal places during multiplication.
Once you have your whole number product, you'll correct the decimal placement at the end.

Placing Decimal in the Product

After multiplying the numbers as if they were whole numbers, it's time to position the decimal appropriately in your product.
This involves counting the total decimal places from the original numbers—in this case, four.
With a product of 18 from our decimal-free multiplication, you adjust by envisioning it as a four-decimal-place number: 000018.

• Start at the right of 18.
• Move four places left.

This gives you 0.0018.
If necessary, add zeros to maintain the correct number of decimal places, ensuring the product accurately reflects the original problem's decimal structure.