10.66666666667 as a Fraction

Answer

The answer for 10.66666666667 as a fraction will be 32/3.

Explanation

Converting a recurring decimal to a fraction can be a straightforward task. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 10.66666666667. Notice that the decimal part 0.66666666667 is repeating.

Step 2: Multiply x by 10 to shift the decimal point: 10x = 106.66666666667.

Step 3: Subtract the original x from this equation to eliminate the repeating part: 10x - x = 106.66666666667 - 10.66666666667 9x = 96

Step 4: Solve for x by dividing both sides by 9: x = 96/9

Step 5: Simplify the fraction by finding the GCD of 96 and 9, which is 3. Divide the numerator and denominator by their GCD: 96/9 = 32/3

Thus, 10.66666666667 can be written as a fraction 32/3.

• 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.
   
• Recurring Decimal: A decimal in which one or more digits repeat 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.