2.66666 as a Fraction

Answer

The answer for 2.66666 as a fraction will be 8/3.

Explanation

Converting a repeating decimal to a fraction involves a few steps. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 2.66666..., which is a repeating decimal. In this case, 6 is the repeating digit.

Step 2: Multiply both sides of the equation by 10 to move the decimal point one place to the right: 10x = 26.66666...

Step 3: Subtract the original equation (x = 2.66666...) from this new equation (10x = 26.66666...) to eliminate the repeating part: 10x - x = 26.66666... - 2.66666...

Step 4: Simplify the equation: 9x = 24

Step 5: Solve for x by dividing both sides by 9: x = 24/9

Step 6: Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 3: 24/9 = 8/3

Thus, 2.66666 can be written as a fraction 8/3.

• Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
   
• Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.
   
• Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.
   
• Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.
   
• Denominator: The bottom part of a fraction, showing how many parts make up a whole.