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Last updated on August 5, 2025

0.66666 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. A fraction is one of its kinds. It is always represented in the form of p/q, where p is the numerator and q is the denominator. A fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2; numbers in decimal are expressed with a decimal point (.), for example, 0.66666. We are going to learn how to convert a repeating decimal to a fraction.

0.66666 as a Fraction for US Students
Professor Greenline from BrightChamps

What is 0.66666 as a Fraction?

0.66666 as a fraction

Answer

 

The answer for 0.66666 as a fraction will be 2/3.

 

Explanation

 

Converting a repeating decimal to a fraction can be done through a few steps. You can follow the steps mentioned below to find the answer.

 

Step 1: Let x = 0.66666... (where the 6 repeats infinitely).

 

Step 2: Multiply both sides by 10 to shift the decimal point one place to the right: 10x = 6.66666...

 

Step 3: Now, subtract the original x from this equation to eliminate the repeating decimal: 10x - x = 6.66666... - 0.66666... 9x = 6

 

Step 4: Solve for x by dividing both sides by 9: x = 6/9

 

Step 5: Simplify the fraction by finding the GCD of 6 and 9, which is 3: 6/9 = 2/3

 

Thus, 0.66666 can be written as a fraction 2/3.

Professor Greenline from BrightChamps

Important Glossaries for 0.66666 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.

 

  • Repeating Decimal: A decimal that has one or more repeating digits after the decimal point 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.
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