0.666666666667 as a Fraction

Answer

The answer for 0.666666666667 as a fraction is approximately 2/3.

Explanation

Converting a repeating decimal to a fraction can seem challenging, but it can be done using a simple process. Follow the steps below to find the answer.

Step 1: Identify the repeating part of the decimal. Here, 0.666666666667 has a repeating decimal of 6.

Step 2: To convert a repeating decimal to a fraction, denote the repeating decimal as x. So, let x = 0.666666666667.

Step 3: Multiply both sides by 10 to move the decimal one place right: 10x = 6.666666666667

Step 4: Subtract the original x from this equation: 10x - x = 6.666666666667 - 0.666666666667 9x = 6

Step 5: Solve for x by dividing both sides by 9: x = 6/9

Step 6: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3: 6/9 = 2/3

Thus, 0.666666666667 can be approximated as the fraction 2/3.

• 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 sequence 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.