Question

Convert $\frac{4}{9}$ to a decimal.

• A. $0.3\overline{5}$
• B. $0.\overline{3}$
• C. $0.4\overline{5}$
• D. $0.\overline{4}$

Answer 1

The correct option is D $0.\overline{4}$

$\frac{4}{9}$ represents $4÷9.$

Step 1: Here, denominator > numerator. We have to make the dividend digit (4) greater than the numerator digit (9) by placing 0 next to the 4 and to the quotient respectively. Now we have 40 as a new dividend. (40 > 9).


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

Step 3: Multiply 9 with a number so that the product is less than or equal to 40. $9\times 4=36$. Now, the quotient is 4 and the remainder left is 4.

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

Step 4: Now the new dividend is 40. Multiply 9 with a number so that the product is less than or equal to 40. $9\times 4=36$. Here now the quotient is 4 and the leftover remainder is 4.After introducing decimal in the quotient we can introduce one 0 at each step of division.


Step 5: Again the new dividend is 40. Multiply 9 with a number so that the product is less than or equal to 40. $9\times 4=36$. Here now the quotient is 4 and the leftover remainder is 4.

No matter how long we divide, the 4 will continue to repeat in our quotient. Hence, we write a bar over the repeating digits to show that they repeat.

$\therefore \frac{4}{9}$ can be written as $0.\overline{4}.$