10.66666 as a Fraction

Professor Greenline Explaining Math Concepts

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Numbers can be categorized into different types. A 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. A 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, 10.66666, we are going to learn how to convert a decimal to a fraction.

What is 10.66666 as a Fraction?

$10.66666 as a fraction$

Answer

The answer for 10.66666 as a fraction is 32/3.

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, any decimal number should be converted to a fraction for easy calculation. Here, 10.66666 has a repeating decimal (6), so we represent it as 10.6̅.

Step 2: Let x = 10.6̅. Multiply both sides by 10 to move the decimal point to the right of the repeating part: 10x = 106.6̅.

Step 3: Subtract the original x from this equation to eliminate the repeating part: 10x - x = 106.6̅ - 10.6̅ 9x = 96

Step 4: Solve for x by dividing both sides by 9: x = 96/9 Step 5: Simplify the fraction by finding the GCD of 96 and 9, which is 3. 96/9 = 32/3

Thus, 10.66666 can be written as a fraction 32/3.

Important Glossaries for 10.66666 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 in which a digit or group of digits repeats 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.