3.666666667 as a Fraction

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Numbers can be categorized into different types. Fraction is one of its kind. It is always represented in the form of p/q, where p is the numerator and q is the denominator. Fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 3.666666667, we are going to learn how to convert a decimal to a fraction.

What is 3.666666667 as a Fraction?

$3.666666667 as a fraction$

Answer

The answer for 3.666666667 as a fraction will be 11/3.

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, recognize that 3.666666667 is a repeating decimal. The repeating part is 6, so it is represented as 3.(6) in repeating form.

Step 2: Let x = 3.666666667. Multiply both sides by 10 to shift one full cycle of the repeating decimal to the left: 10x = 36.66666667.

Step 3: Subtract the original x from this equation to eliminate the repeating part: 10x - x = 36.66666667 - 3.666666667 9x = 33

Step 4: Solve for x by dividing both sides by 9: x = 33/9

Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 33/9 = 11/3

Thus, 3.666666667 can be written as a fraction 11/3.

Important Glossaries for 3.666666667 as a Fraction

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 in which a digit or group of digits repeats infinitely.