In your virtual notebook, answer the following questions:
What are the similarities and differences between a natural number, whole number, and integers?
Similarities: A natural number, whole number and integers all have positive whole numbers, meaning they also have no fractions. Differences: A Natural number does not contain zero as do the other two. Integers contain negative unlike the other two. And Whole numbers include zero.
What is the difference between a rational and irrational number?
Rational numbers are numbers including natural numbers, whole numbers and integers, plus all fractions that are terminating decimals. An irrational number is the opposite, its all numbers/fractions that are continuous. Like Pi.
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.
False, because it can be equal to one, the recipricol of 1/1 is equal to one, so it's not less.
True or False: An integer is a rational number. Explain your answer and use an example if necessary.
True. All integers, whole numbers and real numbers are rational numbers.
True or False: A rational number is an integer. Explain your answer and use an example if necessary.
True sometimes, because not all rational numbers are integers but some are.
True or False: A number is either rational or irrational, but not both. Explain your answer and use an example if necessary.
True, because rational and irrational are opposites of eachother.
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)
4.5 and 9/2
A rational number that is infinitely repeating(represented in both fraction and decimal form)
6.66666666... and 20/3
A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category
Three because it fits in the natural numbers, whole numbers, the first two because its a opsitive whole number integers because it is a positive or negative whole number and rational numbers because 3/1 doesnt repeat itself. Unit 1 Lesson 2
In your virtual notebook, answer the following questions:
What is the difference from using brackets [] and parenthesis () in interval notation. How does this notation relate to graphing an inequality?
Brackets mean that it is either less than or more than PLUS equal to, and parenthesis means it is only either less than or more than.
What is the difference between a bounded and unbounded interval?
Bounded has two endpoints, and Unbounded has one or less.
What is the reasoning for only using parenthesis when infinity is included in your interval?
Because infinity is not a real number so it can not be a real end point.
Give an example of a bounded interval and an unbounded interval. Represent the interval as an inequality and verbal. You may not use an example shown in your reading.
1 is less than or equal to y is less than 2 [1, 2) 1 < (or equal to) y < 2 y is less than 3 (- infinity, 3) y < 3
In your virtual notebook, answer the following questions:
- What are the similarities and differences between a natural number, whole number, and integers?
Similarities: A natural number, whole number and integers all have positive whole numbers, meaning they also have no fractions.Differences: A Natural number does not contain zero as do the other two. Integers contain negative unlike the other two. And Whole numbers include zero.
- What is the difference between a rational and irrational number?
Rational numbers are numbers including natural numbers, whole numbers and integers, plus all fractions that are terminating decimals. An irrational number is the opposite, its all numbers/fractions that are continuous. Like Pi.- 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.
False, because it can be equal to one, the recipricol of 1/1 is equal to one, so it's not less.- True or False: An integer is a rational number. Explain your answer and use an example if necessary.
True. All integers, whole numbers and real numbers are rational numbers.- True or False: A rational number is an integer. Explain your answer and use an example if necessary.
True sometimes, because not all rational numbers are integers but some are.- True or False: A number is either rational or irrational, but not both. Explain your answer and use an example if necessary.
True, because rational and irrational are opposites of eachother.- Give an example of a real number set that includes the following elements:
- A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category
Three because it fits in the natural numbers, whole numbers, the first two because its a opsitive whole number integers because it is a positive or negative whole number and rational numbers because 3/1 doesnt repeat itself.- A rational number that is terminating (represented in both fraction and decimal form)
4.5 and 9/2- A rational number that is infinitely repeating(represented in both fraction and decimal form)
6.66666666... and 20/3Unit 1 Lesson 2
In your virtual notebook, answer the following questions:
- What is the difference from using brackets [] and parenthesis () in interval notation. How does this notation relate to graphing an inequality?
Brackets mean that it is either less than or more than PLUS equal to, and parenthesis means it is only either less than or more than.- What is the difference between a bounded and unbounded interval?
Bounded has two endpoints, and Unbounded has one or less.- What is the reasoning for only using parenthesis when infinity is included in your interval?
Because infinity is not a real number so it can not be a real end point.- Give an example of a bounded interval and an unbounded interval. Represent the interval as an inequality and verbal. You may not use an example shown in your reading.
1 is less than or equal to y is less than 2 [1, 2) 1 < (or equal to) y < 2y is less than 3 (- infinity, 3) y < 3