Problem 27 - Prealgebra

Question

Change each decimal to a percent. $$0.03$$

Step-by-Step Solution

Answer

The decimal 0.03 is equivalent to 3%.

Step 1: Understanding the Conversion

To convert a decimal to a percent, we need to recognize that 1 whole in decimal (1.00) is equal to 100% in percent. So, converting any decimal to percent involves multiplying the decimal by 100.

Step 2: Multiply by 100

Multiply the given decimal by 100 to change it to a percentage. For 0.03: \( 0.03 \times 100 = 3 \).

Step 3: Add the Percent Sign

After multiplying, append the percent sign (%) to the number you obtained. So, the result for 0.03 is 3%.

Key Concepts

Percent Conversion

Percent conversion is the process of changing a number from its decimal form into a percentage. This transformation is grounded in the relationship between decimals and percentages, which signifies that moving from a decimal to a percent involves scaling up by a factor of 100. This principle is based on the idea that a whole, or 100%, in percentages is equivalent to 1 in decimal form. Therefore, whenever you need to convert a decimal to a percent, simply multiply the decimal by 100. For example, when dealing with the decimal 0.03, multiplying by 100 yields 3, thus transforming it into a percentage. To complete the conversion, just affix the percent symbol (%) to the number to clearly indicate its new form. Hence, 0.03 becomes 3%.

Math Problem Solving

Math problem solving in the context of percent conversion involves identifying the right steps and operations to successfully execute the conversion. It’s crucial to clearly understand the problem you're facing before starting to solve it. In our example, we start by recognizing that the task is to convert 0.03 into a percentage. Each stage of the process, from determining the conversion method to performing the multiplication, is crucial. Key skills in mathematical problem solving include:

• Reading the problem carefully.
• Identifying what type of problem it is.
• Planning how to solve it.
• Carrying out the planned calculations.
• Reviewing the steps and verification of the solution.

The step-by-step solution begins with comprehending the core principle of percent conversion, followed by the practical operation of multiplying by 100 and then finalizing the result with the percent sign. Each phase validates our understanding of the problem.

Basic Arithmetic Operations

Basic arithmetic operations are the foundational mathematical processes that include addition, subtraction, multiplication, and division. In percent conversion, multiplication is the primary operation used. It’s necessary to multiply the decimal number by 100 to change it into a percent value. This simple operation plays a crucial role in ensuring accuracy. In the case of our exercise, the operation involved multiplying the decimal 0.03 by 100. Multiplication follows basic arithmetic rules that help maintain precision in calculations:

• Ensure understanding of decimal placements.
• Always double-check the operation process.
• Use multiplication as a tool to enlarge the number appropriately within the context given.

These practices ensure that no errors are made during the conversion. It highlights how essential multiplication is not just in isolated operations but as an integral component of solving various mathematical problems accurately.