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….

• 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.