3.166666667 as a Fraction

Answer

The answer for 3.166666667 as a fraction will be 19/6.

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: Identify the repeating part of the decimal. Here, 0.166666667 is the repeating part with '6' repeating. We can write it as 3.1(6).

Step 2: Let x = 3.166666667. Multiply by 10 to shift the repeating part: 10x = 31.66666667.

Step 3: Multiply by 10 again to shift the repeating part after the decimal point: 100x = 316.6666667.

Step 4: Subtract the two equations: 100x - 10x = 316.6666667 - 31.6666667, which simplifies to 90x = 285.

Step 5: Solve for x: x = 285/90.

Step 6: Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 15: 285/90 = 19/6.

Thus, 3.166666667 can be written as a fraction 19/6.

• 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 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.