0.818181 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. 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, 0.818181, we are going to learn how to convert a decimal to a fraction.

What is 0.818181 as a Fraction?

$0.818181 as a fraction$

Answer

The answer for 0.818181 as a fraction is 9/11.

Explanation

Converting a repeating decimal to a fraction involves a slightly different process. You can follow the steps mentioned below to find the answer.

Step 1: Let x = 0.818181... (where 81 is repeating).

Step 2: Multiply both sides by 100 to shift the decimal point two places to the right (because the repeating part is two digits long). 100x = 81.818181...

Step 3: Now, subtract the original equation (x = 0.818181...) from this new equation: 100x - x = 81.818181... - 0.818181...

Step 4: This gives us: 99x = 81

Step 5: Solving for x, we have: x = 81/99

Step 6: Simplify the fraction by finding the GCD of 81 and 99, which is 9. 81/99 = 9/11

Thus, 0.818181 can be written as a fraction 9/11.

Important Glossaries for 0.818181 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.

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.

Simplification: The process of reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).