102 LearnersLast updated on May 26th, 2025
7.66666666667 as a Fraction
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. Fractions represent a whole and a fractional part. Decimals represent the fractional part of numbers. For example, in 1/2, numbers in decimal are expressed with a decimal point (.), like 0.5. We are going to learn how to convert a decimal to a fraction using the example of 7.66666666667.
What is 7.66666666667 as a Fraction?
Answer
The answer for 7.66666666667 as a fraction will be 23/3.
Explanation
Converting a repeating decimal to a fraction involves a few steps. You can follow the steps mentioned below to find the answer.
Step 1: Let x = 7.66666666667. Notice that the decimal part 0.666666... repeats.
Step 2: Multiply x by 10 to shift the decimal point: 10x = 76.6666666667.
Step 3: Subtract the original x from this equation to remove the repeating part: 10x - x = 76.6666666667 - 7.66666666667, resulting in 9x = 69.
Step 4: Solve for x by dividing both sides by 9: x = 69/9.
Step 5: Simplify the fraction by finding the GCD (Greatest Common Divisor) of 69 and 9, which is 3. 69/9 = 23/3
Thus, 7.66666666667 can be written as a fraction 23/3.
Important Glossaries for 7.66666666667 as a Fraction
- Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
- Repeating Decimal: A decimal that has one or more repeating digits after the decimal point.
- 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.
- Greatest Common Divisor (GCD): The largest number that can divide two numbers without leaving a remainder.
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