Question

Which of the following represent a decimal $\frac{12}{99}$

• A. terminating decimal
• B. non-terminating and repeating decimal with 1 as repeating digit
• C. non-terminating and repeating decimal with 12 as repeating digits
• D. none of the above

Answer 1

The correct option is C non-terminating and repeating decimal with 12 as repeating digits

Let's convert $\frac{12}{99}$ to a decimal.

$\frac{12}{99}$ represents $12÷99.$

Step 1: Here, denominator > numerator.

We have to make the dividend digit (12) greater than the numerator digit (99) by placing 0 next to the 12 and to the quotient respectively.

Now we have 120 as a new dividend. (120 > 99).

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

Step 3: No matter how long we divide, 12 will continue to repeat in the quotient. So, we write a bar in order to show the recurring digits.

$\therefore \frac{12}{99}$ can be written as $0.\overline{12},$ which is non-terminating and repeating decimal with 12 as repeating digits