To which of the following number systems does the decimal −3.162 NOT belong?
Select one:
A. Integers
B. Rational Numbers
C. Real Numbers
D. Complex Numbers
.162 means NOT an integer
−3.162 = -3162/1000 so IS rational
no square root of -1 = i in there so IS real
only if you have an i in there it is complex. It is NOT
well, I suppose you could have −3.162 + 0 i
To determine which number system the decimal −3.162 does not belong to, we need to understand the properties of each number system.
A. Integers: Integers are whole numbers that can be positive, negative, or zero. In this case, −3.162 is a negative decimal, which means it can also be written as -3.162. Therefore, it can be classified as an integer.
B. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. This includes both terminating and repeating decimals. Since -3.162 can be expressed as -3162/1000, it can be classified as a rational number.
C. Real Numbers: Real numbers are numbers that include all rational and irrational numbers. -3.162 can be considered a rational number, as explained before, and thus it is a real number.
D. Complex Numbers: Complex numbers are numbers that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). Since the decimal -3.162 does not have an imaginary component, it cannot be classified as a complex number.
Therefore, the correct answer is D. Complex Numbers.