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Last updated on May 26th, 2025

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7.66666666667 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. 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.

7.66666666667 as a Fraction for Australian Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Australia

At BrightChamps, we know math questions are more than just numbers—they open doors to countless opportunities! Our goal is to help kids all across Australia develop essential math skills, focusing today on the 7.66666666667 as a Fraction with a special focus on fraction conversions—in an engaging, fun, and easy-to-follow way. Whether your child is figuring out how fast a roller coaster speeds through Luna Park Sydney, tracking scores at a local cricket match, or managing their allowance for the latest gadgets, confident math skills prepare them for everyday challenges. Our interactive lessons make learning straightforward and enjoyable. Since kids in Australia learn in many different ways, we tailor our approach to fit each child’s unique style. From Sydney’s vibrant streets to the stunning beaches of the Gold Coast, BrightChamps brings math to life, making it relevant and exciting throughout Australia. Let’s make fraction conversions a fun part of every child’s math journey!
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