3.66666 as a Fraction

Answer

The answer for 3.66666 as a fraction will be 11/3.

Explanation

Converting a repeating decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 3.66666... (recurring).

Step 2: Multiply both sides by 10 to eliminate the repeating part. 10x = 36.66666...

Step 3: Subtract the original equation (x = 3.66666...) from this new equation. 10x - x = 36.66666... - 3.66666... 9x = 33

Step 4: Solve for x by dividing both sides by 9. x = 33/9

Step 5: Simplify the fraction by dividing the numerator and the denominator by their GCD, which is 3. 33/9 = 11/3

Thus, 3.66666 can be written as a fraction 11/3.

• 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.
   
• 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.
   
• Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.