3.11111111111 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, 3.11111111111, we are going to learn how to convert a decimal to a fraction.

What is 3.11111111111 as a Fraction?

$3.11111111111 as a fraction$

Answer

The answer for 3.11111111111 as a fraction will be 28/9.

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: Firstly, separate the whole number from the decimal. Here, 3 is the whole number.

Step 2: Recognize the repeating decimal part, which is 0.11111111111. This is a repeating decimal.

Step 3: Convert the repeating decimal to a fraction. Let x = 0.11111111111... Then, 10x = 1.11111111111... Subtract the first equation from the second: 10x - x = 1.11111111111... - 0.11111111111... 9x = 1 x = 1/9 Therefore, 0.11111111111... = 1/9.

Step 4: Add the whole number to the fraction. 3 + 1/9 = 27/9 + 1/9 = 28/9

Thus, 3.11111111111 can be written as a fraction 28/9.

Important Glossaries for 3.11111111111 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 fraction in which a figure or group of figures is repeated indefinitely.
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.