How do you convert 0.26 (6 repeating) to a fraction?

To convert the repeating decimal 0.26 (with 6 repeating) into a fraction, follow these steps:

Step 1: Define the Decimal

Let x equal the repeating decimal:

x = 0.266666...

Step 2: Eliminate the Repeating Part

To isolate the repeating part, multiply x by 10:

10x = 2.66666...

Step 3: Set Up the Equation

Now, subtract the original equation from this new one:

10x - x = 2.66666... - 0.26666...

Which simplifies to:

9x = 2.4

Step 4: Solve for x

Now, divide both sides by 9:

x = 2.4 / 9

Step 5: Convert to Fraction

To express 2.4 as a fraction, recognize that:

2.4 = 24/10 = 12/5

Thus, we have:

x = (12/5) / 9 = 12/45

Step 6: Simplify the Fraction

Now, simplify 12/45:

Both numbers can be divided by 3:

12 ÷ 3 = 4 and 45 ÷ 3 = 15

So, the simplified fraction is:

x = 4/15

Final Result

The decimal 0.26 (6 repeating) can be expressed as the fraction:

4/15