#### Convert 3.5 (repeating) into a fraction.

**Final Answer**

The repeating decimal 3.5 translates to the fraction after a series of algebraic manipulations. By defining the repeating decimal as a variable, we applied multiplication and subtraction to find the solution. This technique is effective for any repeating decimal conversion.

**Explanation**

To convert the repeating decimal 3.5 (which means 3.5555…) into a fraction, we can follow these steps:

Let x = 3.5 (repeating)

Thus, we can represent it as:

x=3.5 (repeating)

Multiply both sides by 10 to shift the decimal:

10x=35.5 (repeating)

Now, we have two equations:

Equation 1: x=3.5 (repeating)

Equation 2: 10x=35.5 (repeating)

Subtract the first equation from the second to eliminate the repeating part:

10x−x=35.5−3.5

9x=32

Solve for x by dividing both sides by 9:

x=

Thus, the fraction equivalent of 3.5 (repeating) is . This method works well for converting any repeating decimal into a fraction.

Examples & Evidence

For more examples of converting repeating decimals to fractions, consider the decimal 0.3 (repeating), which can be expressed as . Similarly, 2.1 (repeating) converts to . These illustrate how to use the same methodology to simplify other repeating decimals.

This process is a standard algebraic method for converting repeating decimals, widely taught in high school mathematics. Each step utilizes fundamental algebraic principles, ensuring accuracy in the conversion.

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