7.66666666667 as a Fraction

Answer

The answer for 7.66666666667 as a fraction will be 23/3.

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 = 7.66666666667. Notice that the decimal part 0.666666... repeats.

Step 2: Multiply x by 10 to shift the decimal point: 10x = 76.6666666667.

Step 3: Subtract the original x from this equation to remove the repeating part: 10x - x = 76.6666666667 - 7.66666666667, resulting in 9x = 69.

Step 4: Solve for x by dividing both sides by 9: x = 69/9.

Step 5: Simplify the fraction by finding the GCD (Greatest Common Divisor) of 69 and 9, which is 3. 69/9 = 23/3

Thus, 7.66666666667 can be written as a fraction 23/3.

• Fraction: A numerical quantity that is not a whole number, representing a part of a whole.

• Repeating Decimal: A decimal that has one or more repeating digits after the decimal point.

• 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.

• Greatest Common Divisor (GCD): The largest number that can divide two numbers without leaving a remainder.