8.66666666667 as a Fraction

Answer

The answer for 8.66666666667 as a fraction is 26/3.

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 equal the repeating decimal number, so x = 8.66666666667.

Step 2: Identify the repeating part of the decimal. Here, 6 is the repeating digit.

Step 3: Multiply the entire equation by 10 to the power of n, where n is the number of repeating digits. In this case, n = 1, so multiply by 10: 10x = 86.6666666667

Step 4: Subtract the original equation (x = 8.66666666667) from this new equation: 10x - x = 86.6666666667 - 8.66666666667 9x = 78

Step 5: Solve for x: x = 78/9

Step 6: Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 3: 78/9 = 26/3

Thus, 8.66666666667 can be written as the fraction 26/3.

• 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 that has one or more repeating digits after the decimal point.