0.888888889 as a Fraction

Answer:

The answer for 0.888888889 as a fraction will be 8/9.

Explanation:

Converting a repeating decimal to a fraction can be done easily by following these steps.

Step 1: Let x = 0.888888889. Since the decimal repeats every 9 digits, multiply x by 1,000,000,000 to shift the decimal point: 1,000,000,000x = 888,888,889.0

Step 2: Subtract the original equation from this new equation to eliminate the repeating decimal: 1,000,000,000x - x = 888,888,889.0 - 0.888888889 999,999,999x = 888,888,888.111111111

Step 3: Solve for x by dividing both sides by 999,999,999: x = 888,888,888.111111111 / 999,999,999

Step 4: Simplify the fraction. The GCD of 888,888,888 and 999,999,999 is 111,111,111. 888,888,888 / 999,999,999 = 8/9

Thus, 0.888888889 can be written as a fraction 8/9.

• 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 a 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.