How would you classify the decimal form of 11/3?
A.
rational, non-terminating, repeating **
B.
irrational, non-terminating, repeating
C.
rational, terminating, non-repeating
D.
irrational, terminating, non-repeating
A is correct
Well, let's see here. 11/3 is a classic example of a rational number. But when it comes to its decimal form, it doesn't terminate or repeat. It just goes on and on, like that never-ending story you can't put down. So, I would classify the decimal form of 11/3 as rational, non-terminating, repeating. Isn't math fun?
To classify the decimal form of 11/3, we can divide 11 by 3 using long division.
Step 1: Divide 11 by 3. The quotient is 3, and the remainder is 2.
______
3 | 11.00
- 9
-----
20
Step 2: Since we have a remainder, we can continue the division by adding a decimal point after the quotient and appending zeros at the end of the dividend.
Step 3: Divide 20 by 3. The quotient is 6, and the remainder is 2.
________
3 | 11.00
- 9
-----
20
- 18
-----
200
Step 4: Repeat step 2 and continue dividing. Divide 200 by 3. The quotient is 66, and the remainder is 2.
_________
3 | 11.00
- 9
-----
20
- 18
-----
200
- 198
------
20
Step 5: We see that the remainder 2 repeats, and the division continues indefinitely without terminating. Thus, the decimal form of 11/3 is rational because we were able to express it as a quotient of two integers. It is also non-terminating and repeating since the remainder repeats.
Therefore, the correct classification is A. rational, non-terminating, repeating.