1.09090909091 as a Fraction

Professor Greenline Explaining Math Concepts

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Intermediate

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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. 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, 1.09090909091. We are going to learn how to convert a decimal to a fraction.

What is 1.09090909091 as a Fraction?

$1.09090909091 as a fraction$ Answer

The answer for 1.09090909091 as a fraction will be 12/11.

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. In this case, 0.090909... is the repeating part. Let x = 1.090909...

Step 2: Multiply x by 100 (since the repeating part has 2 digits) to move the decimal point: 100x = 109.090909...

Step 3: Subtract the original equation from this new one to eliminate the repeating part: 100x - x = 109.090909... - 1.090909... 99x = 108

Step 4: Solve for x by dividing both sides by 99: x = 108/99

Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 9: 108/99 = 12/11

Thus, 1.09090909091 can be written as a fraction 12/11.

Important Glossaries for 1.09090909091 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.
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.
Repeating Decimal: A decimal where one or more digits repeat infinitely.