Problem 23 - Prealgebra

Question

Find each of the following products. $$\begin{array}{r} 0.0043 \\ \times 100 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

The product is 0.43.

Step 1: Understanding Multiplication by 100

When multiplying a number by 100, we effectively shift the decimal point in the number two places to the right. This is because 100 has two zeros, which corresponds to moving the decimal point two positions.

Step 2: Apply the Shift to the Number

Take the number 0.0043. To multiply by 100, move the decimal point two places to the right. Starting from 0.0043, move it two spaces to get 0.43.

Step 3: Result

After moving the decimal point, the number becomes 0.43. So, the product of 0.0043 and 100 is 0.43.

Key Concepts

Multiplying by Powers of Ten

When dealing with multiplication by powers of ten, such as 10, 100, or 1000, it is simplified by noticing the number of zeros in the power of ten. These zeros tell us how many places we should move the decimal point in the original number, making multiplication straightforward without the need for complex calculations. For example, multiplying by 10 means moving the decimal one place to the right, multiplying by 100 means moving it two places, and multiplying by 1000 means moving it three places. This property is incredibly useful in basic arithmetic and particularly practical for multiplying with decimals to quickly adjust the scale of the number.

Decimal Point Movement

The key when multiplying decimals, especially by ten, is the movement of the decimal point. Understanding this move is crucial for grasping the multiplication process.
When we say move the decimal point to the right, we are actually increasing the number's value. In our example, 0.0043 multiplied by 100 results in a movement of the decimal point two places to the right. As we move the decimal, we discover the number 0.43. This transformation helps to easily visualize shifts in value without needing to perform direct multiplication on each digit.
Mastering this simple shift method is essential when multiplying by any power of ten, as it cuts down potential mistakes and boosts computational speed.

Basic Arithmetic Operations

Basic arithmetic operations, including addition, subtraction, multiplication, and division, form the foundation of math studies. Multiplying decimals can sometimes be challenging compared to whole numbers, but with understanding the specific rules, like the movement of the decimal point, it becomes manageable.
In multiplication, ensure to accurately shift the decimal as detailed earlier, and do not let it be confused with directly handling each digit. By breaking problem-solving into operational steps as discussed, complex-seeming tasks become more straightforward.

• First, identify the power of ten you're working with.
• Second, count the zeros to determine the shift.
• Third, move the decimal point accordingly.

Practicing these basic arithmetic operations increases confidence and skill in handling more advanced problems and ensures a robust foundation in mathematics.