Question

Check each set that includes the number shown.

-17
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers​

Answer 1

Integers, rational numbers and real numbers

Step-by-step explanation:

• Natural numbers are those we use to count: 1, 2, 3, ... etc. So -17 is not included in this set of numbers because it is negative.

• Whole numbers are the natural numbers plus the zero, so -17 is also not a whole number.

• Integers are the whole numbers plus the negative numbers: ...- 2, -1, 0, 1, 2, 3, ... etc. So this set does include -17.

• Rational numbers are those that can be represented as a fraction between two integers
  `(A)/(B)`, so the set of rational numbers includes the integers. Some examples are:
  `(1)/(2)`,
  `(-5)/(3)`,
  `(13)/(1)`, ... Since -17 can be represented as a fraction(
  `(-17)/(1)`) It is a rational number.

• Irrational numbers are those that have non-periodic infinite decimals, such as
  `\pi`,
  `e`, among others. So -17 is not an irrational number.

and finally,

• the real numbers is the grouping of all the aforementioned sets, so since -17 belongs to the rational numbers, it also belongs to the real numbers.