3 divided by 11 what is the long division to convert to a decimal

Answer 1

To divide 3 by 11 using long division and convert it to a decimal, follow these steps:

1. Set up the long division: Place 3 (the dividend) under the long division bar and 11 (the divisor) outside of it.

2. Since 3 is less than 11, we cannot divide it directly. We need to use decimal places. Add a decimal point and zeros to the dividend 3. So, we will consider it as 3.000 (adding zeros allows us to divide into decimal places).

3. Now, consider 30 (the first zero after the decimal). Determine how many times 11 can go into 30:

   • 11 goes into 30 two times because \( 11 \times 2 = 22 \).
   • Write down 2 in the quotient above the long division bar.

4. Subtract \( 22 \) from \( 30 \):

   • \( 30 - 22 = 8 \).

5. Bring down the next 0 (making it 80).

6. Determine how many times 11 goes into 80:

   • 11 goes into 80 seven times because \( 11 \times 7 = 77 \).
   • Write down 7 in the quotient.

7. Subtract \( 77 \) from \( 80 \):

   • \( 80 - 77 = 3 \).

8. Bring down another 0 (making it 30 again).

9. Repeat the process:

   • 11 goes into 30 two times (as calculated before), producing a 2 in the quotient.
   • Subtract and bring down another 0 to get 80.
   • 11 goes into 80 seven times, producing a 7 again.
   • Subtract to get 3 and bring down another 0.

This cycle will repeat indefinitely, resulting in a repeating decimal.

Putting it all together:

• The quotient from our division shows that \( 3 \div 11 = 0.272727... \)

Thus, \( 3 \div 11 = 0.\overline{27} \), indicating that "27" repeats indefinitely.