Answer:
C
Step-by-step explanation:
Let's review some sets of numbers.
Natural numbers: 1, 2, 3, 4, ...
The natural numbers are the counting numbers. You normally start counting with 1, not 0, and you only count whole numbers.
Whole numbers: 0, 1, 2, 3, 4, 5, ...
The whole numbers are the counting numbers with the addition of zero. There are no negative numbers in the whole numbers.
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
The integers are the natural numbers, plus zero, plus the negatives of the natural numbers. All numbers are whole with no decimal part.
Rational numbers
The rational numbers are all numbers that can be written as a fraction of integers. For example, 1 can be written as 3/3, so 1 is a rational number. All natural numbers, whole numbers, and integers are rational numbers. Other rational numbers are numbers that are not whole, such as 2.5, 7/8, 1/4, etc. These numbers can be written as fractions of integers. Rational numbers written as decimal numbers will either be an integer, a terminating decimal, or a non-terminating, repeating decimal.
Up to here, each new set includes the previous set.
Now things change. If a number is rational, it is not irrational.
If a number is irrational, it is not rational.
Irrational numbers
Irrational numbers are always non-terminating, non-repeating decimals. They cannot be written as fractions of integers. Examples: √2, π
Now let's look at this problem.
We have a negative decimal number. The bar above the 12 means the digits 12 are repeating. This number can also be written as -0.121212...
Since our number is a non-terminating, repeating decimal, it is a rational number.
Answer: C
