Problem 54 - Fundamentals of Mathematics

Question

\(0.4 \%\) of what number is \(0.014 ?\)

Step-by-Step Solution

Answer

The number is 3.5.

Step 1: Understand the Problem

We need to find a number such that 0.4% of it equals 0.014.

Step 2: Define the Equation

Let the unknown number be \( x \). We know from the problem statement that 0.4% of \( x \) is equal to 0.014. Therefore, the equation is: \( 0.4\% \times x = 0.014 \).

Step 3: Convert the Percentage to Decimal

Convert 0.4% to a decimal by dividing by 100: \( 0.4\% = \frac{0.4}{100} = 0.004 \).

Step 4: Substitute and Solve for x

Substitute the decimal value into the equation: \( 0.004 \times x = 0.014 \). Solve for \( x \) by dividing both sides by 0.004: \( x = \frac{0.014}{0.004} \).

Step 5: Calculate the Value of x

Perform the division to calculate \( x \): \( x = 3.5 \).

Key Concepts

Equation Solving

Equation solving is a fundamental mathematical skill essential for dealing with percentage problems. When faced with the question, "0.4% of what number is 0.014?" the first step is developing an equation to represent the relationship embodied in the problem.

The equation can be set up as follows: if 0.4% of a number is 0.014, we let the unknown number be represented as \( x \). The equation is then \( 0.004 \times x = 0.014 \). This step is crucial because it translates the word problem into a mathematical problem.

Once the equation is defined, the task is to solve for \( x \). Solving involves isolating \( x \) on one side of the equation, typically by employing basic algebraic operations like division or multiplication. In our scenario, dividing both sides of the equation by 0.004 gives \( x = \frac{0.014}{0.004} \).

Performing this calculation provides the value of \( x \), solving the equation. Mastery of equation solving builds confidence and ensures success in tackling various types of mathematical problems, including percentages.

Decimal Conversion

Decimal conversion is a critical component when working with percentages. Understanding how to convert a percentage to a decimal is essential for solving problems like the one presented here.

When dealing with percentages, "percent" means "per hundred," so converting involves knowing that 0.4% is the same as \( \frac{0.4}{100} \).

This conversion simplifies to \( 0.004 \), which is then used in the equation \( 0.004 \times x = 0.014 \).

This seemingly simple conversion is vital because it aligns the percentage into a format compatible with standard arithmetic operations, paving the way for solving the equation. By practicing this method, students can improve their ability to seamlessly transition between percentages and decimals, a skill that will aid not only in math classes but also in real-life scenarios involving financial calculations, scientific data, and more.

Mathematical Problem Solving

Approaching percentage problems with effective mathematical problem-solving strategies is essential for clarity and accuracy. The exercise here demonstrates a structured approach to problem-solving.

Initially, understanding the problem is a key step. Clearly identifying what is being asked sets the stage for creating an appropriate equation. Next, defining the equation involves applying the underlying relationship in a structured form.

Converting percentages to decimals simplifies the arithmetic, making the problem more manageable. Finally, solving the equation step-by-step allows for systematic progress toward the solution, ensuring each step is understood and each operation is justified.

This organized method not only aids in solving the current problem but also builds general problem-solving skills.

• Identify and understand the problem.
• Translate the problem into an equation.
• Perform necessary conversions for ease.
• Solve the equation systematically.
• Verify the solution for accuracy.

This approach can be applied broadly, reinforcing both comprehension and proficiency in various mathematical contexts.