What are the similarities and differences between a natural number, whole number, and integers?
What is the difference between a rational and irrational number?
Explain if the reciprocal of a positive real number must be less then one. If this statement if false prove your argument with an example and explanation.
True or False: An integer is a rational number. Explain your answer and use an example if necessary.
True or False: A rational number is an integer. Explain your answer and use an example if necessary.
True or False: A number is either rational or irrational, but not both. Explain your answer and use an example if necessary.
Give an example of a real number set that includes the following elements:
A rational number that is terminating (represented in both fraction and decimal form)
A rational number that is infinitely repeating(represented in both fraction and decimal form)
A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category
1. Natural and whole numbers are pretty similar, they both are positive numbers that go from 1 to infinity. Whole numbers include 0, unlike natural numbers. Integers include all of the natural numbers, their opposites (negative numbers), and 0. The integers reach to infinity in both the positive and negative directions. None of these 3 include fractions.
2. Rational can be repeating and terminal fractions/decimals. Irrational numbers are non repeating and non terminating.
3.
4. True
5. True, If an integer is a rational number, a rational number is an integer. (Non-repeating, terminating - can be an integer like 17)
6. True, an irrational number can not be a rational number because it irrational #'s are non repeating and non terminal the exact opposite of rational #'s.
7. Rational Number (Terminating): 1/2 = 0.5
Rational Number (Infinitely): 7/9 = 0.77777...
#2 - real number
- whole number ( it's not a fraction, or a decimal )
- integer
- rational number ( can be written as a fraction 2/1)
1. Natural and whole numbers are pretty similar, they both are positive numbers that go from 1 to infinity. Whole numbers include 0, unlike natural numbers. Integers include all of the natural numbers, their opposites (negative numbers), and 0. The integers reach to infinity in both the positive and negative directions. None of these 3 include fractions.
2. Rational can be repeating and terminal fractions/decimals. Irrational numbers are non repeating and non terminating.
3.
4. True
5. True, If an integer is a rational number, a rational number is an integer. (Non-repeating, terminating - can be an integer like 17)
6. True, an irrational number can not be a rational number because it irrational #'s are non repeating and non terminal the exact opposite of rational #'s.
7. Rational Number (Terminating): 1/2 = 0.5
Rational Number (Infinitely): 7/9 = 0.77777...
#2 - real number
- whole number ( it's not a fraction, or a decimal )
- integer
- rational number ( can be written as a fraction 2/1)