What is 1.6 repeating as a fraction?

To convert the repeating decimal 1.6 (where the 6 repeats indefinitely) into a fraction, follow these steps:

Step 1: Set Up the Equation

Let x equal the repeating decimal:

x = 1.666...

Step 2: Eliminate the Repeating Part

To isolate the repeating part, multiply both sides of the equation by 10:

10x = 16.666...

Step 3: Subtract the Original Equation

Now, subtract the first equation from this new equation:

10x - x = 16.666... - 1.666...

This simplifies to:

9x = 15

Step 4: Solve for x

Now, divide both sides by 9:

x = 15/9

Step 5: Simplify the Fraction

The fraction can be simplified:

x = 5/3

Final Result

Thus, the repeating decimal 1.6 can be expressed as the fraction 5/3.