9.66666666667 as a Fraction

Answer

The answer for 9.66666666667 as a fraction is 29/3.

Explanation

Converting a repeating decimal to a fraction is a task that can be done by following these steps:

Step 1: Let x equal the repeating decimal. Here, x = 9.66666666667.

Step 2: Multiply x by a power of 10 that shifts the decimal point to the right so that the repeating part aligns. Since the decimal 6 repeats, multiply by 10 to get 10x = 96.6666666667.

Step 3: Subtract the original equation (x = 9.66666666667) from this new equation: 10x - x = 96.6666666667 - 9.66666666667 9x = 87

Step 4: Solve for x: x = 87/9 x = 29/3

Thus, 9.66666666667 can be written as the fraction 29/3.

• 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.