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Chapter 4: Problem 8

Multiply. $$ \begin{array}{r} 18.4 \\ \times 0.07 \\ \hline \end{array} $$

Short Answer

Expert verified
1.288

Step by step solution

01

Remove the decimals

First, temporarily remove the decimal points from the numbers. For 18.4, shift the decimal one place to the right to get 184. For 0.07, shift the decimal two places to the right to get 7.
02

Multiply the whole numbers

Now, multiply the numbers as if they are whole numbers: 184 multiplied by 7.
03

Perform the multiplication

Calculate the product: 184 multiplied by 7 equals 1288.
04

Adjust for the decimal places

Now, count the total number of decimal places from the original numbers. There was one decimal place from 18.4 and two decimal places from 0.07, for a total of three decimal places. Insert the decimal point three places from the right in 1288, which gives 1.288.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplication steps
When dealing with decimal multiplication, follow a clear, step-by-step process to avoid errors.
First, you should convert the decimals into whole numbers. For example, to multiply 18.4 by 0.07, shift the decimal in 18.4 one place to the right to get 184, and shift the decimal in 0.07 two places to the right to get 7.
Next, multiply these whole numbers: 184 multiplied by 7. The result is 1288.
Lastly, don't forget to adjust the decimal places back to their original positions. The correct placement of decimals ensures the accuracy of your final product.
adjusting decimal places
To accurately multiply decimal numbers, it's crucial to properly adjust the decimal places. Start by counting the number of decimal places in each original number.
In our example, 18.4 has one decimal place and 0.07 has two decimal places; combined, that鈥檚 three decimal places.
After doing the multiplication (184 multiplied by 7 equals 1288), reintroduce the decimal point by moving it three places from the right. This adjustment turns 1288 into 1.288.
By carefully managing decimal places, you maintain the integrity of your calculations.
basic arithmetic
Understanding basic arithmetic is fundamental for mastering decimal multiplication. Basic arithmetic involves operations like addition, subtraction, multiplication, and division.
Familiarizing yourself with multiplication tables can make the multiplication step much easier and faster. In our example, knowing that 184 multiplied by 7 equals 1288 is essential.
Additionally, it's important to be comfortable with shifting decimals and performing these operations in sequence. Consistent practice of these basic skills reinforces your arithmetic foundation, leading to better accuracy and confidence.

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