11.1111111111 as a Fraction

Professor Greenline Explaining Math Concepts

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Intermediate

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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. 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, 11.1111111111, we are going to learn how to convert a decimal to a fraction.

What is 11.1111111111 as a Fraction?

$11.1111111111 as a fraction$

Answer

The answer for 11.1111111111 as a fraction will be 100/9.

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, 11.1111111111 has a repeating "1".

Step 2: Let x = 11.1111111111...

Step 3: Multiply both sides by 10 to shift the decimal point: 10x = 111.1111111111...

Step 4: Subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 111.1111111111... - 11.1111111111... 9x = 100

Step 5: Solve for x: x = 100/9

Thus, 11.1111111111 can be written as the fraction 100/9.

Important Glossaries for 11.1111111111 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.