0.166666666 as a Fraction

Answer

The answer for 0.166666666 as a fraction will be 1/6.

Explanation

Converting a 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: Firstly, the repeating decimal 0.166666666 can be rewritten as 0.1(6) to indicate that the digit 6 is repeating. Let x = 0.166666666...

Step 2: Multiply both sides by 10 to shift the decimal point: 10x = 1.666666666...

Step 3: Subtract the original equation (x = 0.166666666...) from this result: 10x - x = 1.666666666... - 0.166666666...

Step 4: This simplifies to: 9x = 1.5

Step 5: Solve for x by dividing by 9: x = 1.5/9 = 3/18

Step 6: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 3: 3/18 = 1/6

Thus, 0.166666666 can be written as a fraction 1/6.

• 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 fraction 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.