Problem 1 - Prealgebra

Question

In Exercises 1-28, multiply the decimals. (6.7)(0.03)

Step-by-Step Solution

Answer

The product is 0.201.

Step 1: Ignore the Decimal Points

First, ignore the decimal points and consider the numbers as whole numbers. In this case, multiply 67 by 3.

Step 2: Multiply the Whole Numbers

Calculate the product of 67 and 3: \[ 67 \times 3 = 201 \]

Step 3: Count Decimal Places

Count the total number of decimal places in the original numbers. 6.7 has 1 decimal place and 0.03 has 2 decimal places, for a total of 3 decimal places.

Step 4: Apply Decimal Places to the Product

Place the decimal point in the result from Step 2. The number 201 must have 3 decimal places, so write it as 0.201.

Key Concepts

Step-by-Step Solution

Breaking down complex math problems into manageable steps can simplify the process tremendously. Let's explore how a step-by-step solution helps effectively solve decimal multiplication, like the example with 6.7 multiplied by 0.03.

The first step is to ignore the decimal points and treat the numbers as whole numbers. By doing this, you make the calculation straightforward. So, for 6.7 and 0.03, you temporarily convert them to 67 and 3, respectively.

Next, you perform the multiplication of these whole numbers: - Multiply 67 by 3 to get 201.
Let's move on to the decimals. Count the decimal places in the original numbers to understand how to place the decimal point in your answer. 6.7 has 1 decimal place, and 0.03 has 2 decimal places. Adding those gives a total of 3 decimal places. - Finally, apply these decimal places to your product from before. Convert 201 to a decimal number by placing the decimal point, resulting in 0.201.

This structured approach helps keep calculations organized and clear.

Multiplication of Decimals

Multiplying decimals might seem daunting at first, but it's truly a methodical process. To multiply decimals, you'll employ a strategic approach that simplifies calculations.

Start without considering the decimal points. Treat each decimal number as if it were a whole number. Here's why: when you remove the decimal, you're initially reducing a step that could confuse the arithmetic. By multiplying 6.7 and 0.03 as 67 and 3, you get an easy product to manage, which is 201 in this case.

Once you've calculated the product as a whole number, it's important to recognize the role of decimal places. Both numbers have decimals — this must be reflected in your final answer.

• The first number, 6.7, has 1 decimal place.
• The second number, 0.03, has 2 decimal places.

Combine the decimal places, and account for 3 places altogether.

This means the final product should incorporate these 3 places, thus turning your result into 0.201.

Math Problem-Solving

Solving math problems requires a blend of strategy and understanding of basic principles. When tackling a problem involving decimal multiplication, a logical step-by-step solution can aid in finding the correct result.

Consideration of decimal places plays a crucial role. Math problems, like multiplying 6.7 by 0.03, demand accuracy that stems from correctly placing the final decimal.

Problem-solving is about recognizing patterns and applying consistent methods. - Ignoring decimals initially highlights the numbers' core arithmetic without distraction. - Calculating the straightforward multiplication focuses on obtaining a pure numerical product first. - Revisiting the placement of decimals ensures precision in your answer.

Embracing this method not only aids in this specific type of problem but builds competencies across diverse math problems.

Developing comfort with these techniques can transform complex math challenges into simpler exercises, encouraging confidence and a deeper understanding of the math involved.