23.6666666667 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. Fractions are one of these types. A fraction 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; numbers in decimal form are expressed with a decimal point (.); for example, 23.6666666667. We are going to learn how to convert a repeating decimal to a fraction.

23.6666666667 as a Fraction for US Students

What is 23.6666666667 as a Fraction?

$23.6666666667 as a fraction$ Answer

The answer for 23.6666666667 as a fraction is 71/3.

Explanation

Converting a repeating decimal to a fraction can be done systematically. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 23.6666666667, where the digit 6 repeats indefinitely. So, we recognize this as a repeating decimal.

Step 2: Multiply x by 10 to shift the decimal point: 10x = 236.6666666667...

Step 3: Multiply x by 100 to shift the decimal point two places: 100x = 2366.6666666667...

Step 4: Subtract the equation in Step 2 from the equation in Step 3: 100x - 10x = 2366.6666666667 - 236.6666666667 90x = 2130

Step 5: Solve for x: x = 2130/90

Step 6: Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 30: 2130/90 = 71/3

Thus, 23.6666666667 can be written as the fraction 71/3.

Important Glossaries for 23.6666666667 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.