Problem 20 - Prealgebra

Question

Find each of the following products. $$\begin{array}{r} 0.3 \\ \times 0.02 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

The product is 0.006.

Step 1: Ignore the Decimals

First, perform the multiplication without considering the decimal points. Multiply 3 by 2.

Step 2: Multiply the Numbers

Calculate the product of 3 and 2. This gives you 6.

Step 3: Determine the Total Decimal Places

Count the number of decimal places in both numbers. 0.3 has 1 decimal place, and 0.02 has 2 decimal places, making a total of 3 decimal places.

Step 4: Apply Decimal Places to the Product

Take the product from Step 2, which is 6, and place the decimal point such that there are 3 decimal places. This gives you 0.006.

Key Concepts

Understanding Decimal Places

Decimal places are the digits found to the right of the decimal point in a number. Understanding how many decimal places a number has is crucial when you're working with decimal multiplication.

When you see a number like 0.3, it means one-tenth or 3 out of 10 parts. Hence, there is one decimal place, which is the place of the digit '3' after the decimal point. In another example, 0.02 represents two hundredths, and it has two decimal places. Knowing this helps you determine how precise a number is, and allows you to perform operations accurately.

• One decimal place means the digit is in the tenth place.
• Two decimal places mean the digit is in the hundredth place.
• The more decimal places, the more precision.

Using decimal places consistently is important as it ensures that your calculations reflect the true value of what you're measuring or computing.

The Process of Multiplying Decimals

Multiplying decimals might seem tricky initially, but it's quite straightforward once you understand the process. The basic idea is to first ignore the decimal points and then place them accurately in the final answer.

Imagine you have to multiply 0.3 by 0.02. First, temporarily ignore the decimals, allowing you to multiply 3 by 2. It's a simple multiplication! With decimals ignored, you're left with ordinary numbers, 3 and 2, resulting in a product of 6.

• Write down the numbers without considering the decimal points.
• Multiply them as if they were whole numbers.
• Count the total number of decimal places in the original numbers to use later.

This approach simplifies the process by temporarily removing the complexity the decimal places add, making multiplication manageable.

Accurate Product Calculation by Applying Decimal Places

Once you've performed the basic multiplication ignoring the decimal points, it's time to adjust the product using decimal places to get the accurate result.

In our example, you've obtained a product of 6 by multiplying 3 by 2. However, this isn't the final answer. You need to move the decimal point back into the product based on the original numbers' decimal places. Notice that 0.3 has one decimal place, and 0.02 has two. So, the total number of decimal places is three.

• Count the total decimal places from the original numbers.
• Move the decimal point in the product rightward by this total number of places.
• Produce the final answer, which will be precise based on the original decimals.

Bringing the decimal back ensures your product accurately reflects the size suggested by the original numbers, giving you a precise answer of 0.006 in this case.