Solution By Steps

Step 1: Convert Decimal to Fraction

To convert the repeating decimal 0.61111 to a fraction, let x = 0.61111. Multiply x by 10 to shift the decimal point: 10x = 6.11111.

Step 2: Subtract Equations

Subtract the original equation from the one with the decimal shifted: 10x - x = 6.11111 - 0.61111.

Step 3: Solve for x

Calculate 9x = 5.5 to find the value of x.

Step 4: Convert to Fraction

Since x = 5.5 / 9, the fraction equivalent to 0.61111 is 5.5 / 9.

Step 5: Find Fraction of 0.61111

To find a fraction of 0.61111, multiply 0.61111 by a fraction. Let the fraction be a/b.

Step 6: Set Up Equation

Set up the equation: 0.61111 = 0.61111 * (a/b).

Step 7: Solve for a/b

Solve for a/b: a/b = 5.5 / 9.

Final Answer

A fraction of 0.61111 that is equivalent to the repeating decimal is 5.5 / 9.

Key Concept

Decimal to Fraction Conversion

Key Concept Explanation

Converting a repeating decimal to a fraction involves setting up an equation, solving for the unknown variable, and then expressing the fraction in its simplest form. This process is essential in mathematics and real-world applications where precise values are required.