Problem 265 - Intermediate Algebra

Question

In the following exercises, multiply. $$ (0.025)(100) $$

Step-by-Step Solution

Answer

The result is 2.5.

Step 1: Understand the Problem

The task requires multiplying two numbers: 0.025 and 100.

Step 2: Set Up the Multiplication

Write down the multiplication expression: \(0.025 \times 100\)

Step 3: Simplify the Multiplication

First, notice that multiplying a number by 100 is the same as moving the decimal point two places to the right.

Step 4: Move the Decimal Point

Move the decimal point in 0.025 two places to the right: \(0.025 \rightarrow 2.5\)

Step 5: Verify the Result

Check the movement of the decimal point: \(0.025 \rightarrow 0.25 \rightarrow 2.5\)

Key Concepts

Decimal Multiplication

Decimal multiplication might seem tricky at first, but it becomes simple when you follow steps. When multiplying decimals, consider the number of decimal places: the total number of decimal places in the product is the sum of the decimal places of the numbers being multiplied.
In the exercise, notice we are multiplying 0.025 (which has three decimal places) by 100 (which has zero decimal places).
However, because 100 is a whole number, we're essentially shifting the decimal point of 0.025.
Understand the number of shifts makes it clearer how the decimal will move in the product.

Place Value

Place value is fundamental in understanding multiplication, especially with decimals. Place value helps you comprehend where each digit stands in a number and its respective value.
In our exercise, 0.025 means:

• ‘0’ in the tenths place
  • ‘2’ in the hundredths place
  and
  • ‘5’ in the thousandths place
  When you multiply by 100, you shift each digit two places to the left, converting 0.025 to 2.5. Remember to count the places accurately to avoid mistakes.

Basic Algebra Operations

Basic algebra operations are the building blocks for more complex math problems. Multiplication, a core algebra operation, follows specific rules, even for decimals.
When multiplying decimals with whole numbers, multiply as if both numbers were whole, then place the decimal in the product correctly.
For the task:

• Write the decimal and whole number: 0.025 and 100
• Treat it as: 25 × 100 = 2500
• Add the decimal back: 2.5

This results in 2.5, which demonstrates how algebra principles make solving decimal multiplication straightforward.