0.27272727 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 kinds. 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, 0.27272727, we are going to learn how to convert a decimal to a fraction.

What is 0.27272727 as a Fraction?

$0.27272727 as a fraction$

Answer

The answer for 0.27272727 as a fraction will be 3/11.

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: Identify the repeating part of the decimal. Here, 0.27272727 has a repeating part of 27.

Step 2: Let x = 0.27272727...

Step 3: Multiply both sides of the equation by 100 (since the repeating part has 2 digits): 100x = 27.27272727...

Step 4: Subtract the original equation from this new equation: 100x - x = 27.27272727... - 0.27272727...

Step 5: Simplify to get: 99x = 27

Step 6: Solve for x by dividing both sides by 99: x = 27/99

Step 7: Simplify the fraction by dividing the numerator and denominator by their GCD, which is 9: 27/99 = 3/11

Thus, 0.27272727 can be written as a fraction 3/11.

Important Glossaries for 0.27272727 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.