Final answer:
True statements about the real number system include that integers do not have decimals or fractions, real numbers consist of rational and irrational numbers, rational numbers can be expressed as a ratio, and irrational numbers have non-terminating, non-repeating decimals. Natural numbers are only positive, which makes one of the given statements false.
Step-by-step explanation:
The statements that are true about the real number system include:
- Integers are positive and negative numbers, including zero. But integers do not include decimal or fractional values. This statement is true because integers consist of the set of whole numbers and their opposites, and indeed they do not include fractions or decimals.
- The real number system is made of rational numbers and irrational numbers. This is true because real numbers include all numbers that can be found on the number line, which encompasses both rational and irrational numbers.
- Rational numbers can be written as a ratio. This statement is true because any rational number can be expressed as the quotient of two integers (a fraction) where the denominator is not zero.
- Irrational numbers contain decimal values that neither terminate (do not end) nor repeat in a pattern. This is also true as irrational numbers cannot be expressed as simple fractions and their decimal expansions are non-terminating and non-repeating.
The statement about natural numbers being positive or negative is false. Natural numbers, also known as counting numbers, are always positive and start from 1, going upwards (1, 2, 3, ...).