10.66666666667 as a Fraction

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 10.66666666667, we are going to learn how to convert a decimal to a fraction.

What is 10.66666666667 as a Fraction?

$10.66666666667 as a fraction$

Answer

The answer for 10.66666666667 as a fraction will be 32/3.

Explanation

Converting a recurring decimal to a fraction can be a straightforward task. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 10.66666666667. Notice that the decimal part 0.66666666667 is repeating.

Step 2: Multiply x by 10 to shift the decimal point: 10x = 106.66666666667.

Step 3: Subtract the original x from this equation to eliminate the repeating part: 10x - x = 106.66666666667 - 10.66666666667 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. Divide the numerator and denominator by their GCD: 96/9 = 32/3

Thus, 10.66666666667 can be written as a fraction 32/3.

Important Glossaries for 10.66666666667 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.
Recurring Decimal: A decimal in which one or more digits repeat 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.