0.02 repeating, also known as 0.02 with a bar over the 2, is a decimal that occurs frequently in mathematics and real-world applications. It represents a rational number that can be expressed as a fraction. Understanding how to convert 0.02 repeating to a fraction is essential for various mathematical operations and problem-solving scenarios.

In this article, we will delve into the details of representing 0.02 repeating as a fraction. We will explore different methods, including the geometric approach, the algebraic approach, and the number line method, providing step-by-step instructions for each. Additionally, we will discuss the significance and practical applications of 0.02 repeating as a fraction in different fields.

Converting 0.02 Repeating to a Fraction

Geometric Approach

This method involves dividing a unit square into 100 equal parts. Each part represents a hundredth (0.01). Divide the square into two groups: the shaded region (0.02) and the unshaded region (0.98). Notice that the shaded region is two-hundredths (0.02). Therefore, 0.02 repeating is equivalent to 2/100.

Simplifying the fraction, we get 2/100 = 1/50. Hence, 0.02 repeating as a fraction is 1/50.

Algebraic Approach

Let x represent 0.02 repeating. Multiply both sides of the equation by 100 to clear the decimal: 100x = 2.02. Subtract x from both sides: 99x = 2.00. Solve for x by dividing both sides by 99: x = 2/99. Therefore, 0.02 repeating as a fraction is 2/99.

Number Line Method

Plot 0.02 on the number line. Starting from 0, divide the interval between 0 and 1 into 100 equal parts, each representing a hundredth. Mark the point 0.02, which is two-hundredths away from 0. Notice that the next hundredth mark is 0.03. Therefore, 0.02 is located 2/99 of the way from 0 to 0.03.

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