6.6666666667 as a Fraction

Answer

The answer for 6.6666666667 as a fraction will be approximately 20/3.

Explanation

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

Step 1: Let x = 6.6666666667. Since 6.6666666667 is a repeating decimal (6.6 recurring), you can express it as x = 6.666...

Step 2: Multiply both sides of the equation by 10 (since there is one repeating decimal place) to eliminate the repeating part and form an equation: 10x = 66.666...

Step 3: Now subtract the original equation (x = 6.666...) from this equation to remove the repeating part: 10x - x = 66.666... - 6.666... 9x = 60

Step 4: Solve for x by dividing both sides by 9: x = 60/9

Step 5: Simplify the fraction by finding the GCD of 60 and 9, which is 3: 60/9 = 20/3

Thus, 6.6666666667 can be written approximately as a fraction 20/3.

• 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.