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Last updated on March 5th, 2025

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3 3/11 as a decimal

Professor Greenline Explaining Math Concepts
Foundation
Intermediate
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It is a simple question on decimal conversion. Firstly, we have to learn mixed numbers and decimals. A mixed number consists of a whole number and a fraction. A fraction represents a part of the whole. It has two parts: the numerator (number on the top) and the denominator (number below). A decimal is a way to represent a number that is not whole, using a decimal point to separate the whole part from the fractional part. The numbers to the left of the decimal point represent the whole, and those to the right represent the fractional part.

Professor Greenline from BrightChamps

What is 3 3/11 as a decimal?

3 3/11 as a decimal

Answer

 

3 3/11 in decimals can be written as 3.2727… It is a recurring decimal, indicating that the digits after the decimal point repeat infinitely.

 

Explanation

 

To convert 3 3/11 to a decimal, we will first convert the fraction 3/11 to a decimal. Then, add it to the whole number 3. Let's see the step-by-step breakdown of the process.

 

Step 1: Identify the fraction part 3/11. Here, 3 is the numerator, and 11 is the denominator.

 

 

Step 2: Divide the numerator by the denominator using the long division method.

 

Step 3: As 3 is smaller than 11, we will add a decimal point in the quotient and make it 30.

 

Step 4: Divide 30 by 11. The closest multiple is 11 × 2 = 22, so write 2 in the quotient and subtract 22 from 30 to get 8.

 

Step 5: Bring down another 0 to make it 80, divide by 11 which gives 11 × 7 = 77. Write 7 in the quotient and subtract 77 from 80 to get 3.

 

Step 6: Bring down another 0 and continue the process. The sequence 27 repeats indefinitely, showing it's a recurring decimal.

 

Finally, add the whole number 3 to the decimal obtained from the fraction, giving us 3.2727….

Professor Greenline from BrightChamps

Important Glossaries for 3 3/11 as a decimal

  • Mixed Number: A number consisting of an integer and a proper fraction.
     
  • Fraction: A numerical quantity representing a part of a whole, with a numerator and a denominator.
     
  • Decimal: A number that uses base ten and includes a decimal point to separate the whole part from the fractional part.
     
  • Recurring Decimal: A decimal in which one or more digits repeat infinitely.
     
  • Long Division: A method for dividing numbers to obtain a quotient and remainder, useful in converting fractions to decimals.
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