8.66666 as a Fraction

Professor Greenline Explaining Math Concepts

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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, 8.66666, we are going to learn how to convert a decimal to a fraction.

What is 8.66666 as a Fraction?

$8.66666 as a fraction$

Answer

The answer for 8.66666 as a fraction will be 26/3.

Explanation

Converting a repeating decimal to a fraction can be done by following a few steps. Below are the steps to find the answer.

Step 1: Let x = 8.66666... (This is a repeating decimal where 6 repeats).

Step 2: Multiply both sides by 10 to shift the decimal point: 10x = 86.66666...

Step 3: Subtract the original equation from the new equation to eliminate the repeating part: 10x - x = 86.66666... - 8.66666... 9x = 78

Step 4: Solve for x by dividing both sides by 9: x = 78/9

Step 5: Simplify the fraction 78/9 by finding the GCD, which is 3: 78/9 = (78 ÷ 3)/(9 ÷ 3) = 26/3

Thus, 8.66666 can be written as a fraction 26/3.

Important Glossaries for 8.66666 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.
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.