Question

Convert $\frac{11}{30}$ to a decimal.

• A. $0.\overline{3}$
• B. $0.\overline{36}$
• C. $0.3\overline{6}$
• D. $0.36$

Answer 1

The correct option is C $0.3\overline{6}$

$\frac{11}{30}$ represents $11÷30.$

Step 1: Here, denominator > numerator. We have to make the dividend digit (11) greater than the numerator digit (30) by placing 0 next to the 11 and to the quotient respectively. Now we have 110 as a new dividend. (110 > 30).


Step 2: In the quotient part, it is important to insert decimal (.) after 0 and start the division.

Step 3: Multiply 30 with a number so that the product is less than or equal to 110. $30\times 3=90$. Now, the quotient is 3 and the remainder left is 20.

After introducing decimal in the quotient we can introduce one 0 at each step of division.

Step 4: Now the new dividend is 200. Multiply 30 with a number so that the product is less than or equal to 200. $30\times 6=180$. Here now the quotient is 6 and the leftover remainder is 20.
After introducing decimal in the quotient we can introduce one 0 at each step of division.

Step 5: Again the new dividend is 200. Multiply 30 with a number so that the product is less than or equal to 200. $30\times 6=180$. Here now the quotient is 6 and the leftover remainder is 20.

No matter how long we divide, the 6 will continue to repeat in our quotient. Hence, we write a bar over the repeating digits to show that they repeat.

$\therefore \frac{11}{30}$ can be written as $0.3\overline{6}.$