Identifying and Locating Irrational Numbers, Lecture notes of Pre-Calculus

A lesson on identifying rational and irrational numbers, with a focus on irrational numbers and their properties. It includes statements about the characteristics of irrational numbers, such as repeating decimals and the inability to be written as fractions. The lesson also covers locating irrational numbers on a number line and calculating rational square roots of irrational numbers. Examples and exercises are provided for evaluation.

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2021/2022

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Lesson: Estimating Irrational Numbers
Lesson Topic: Identify rational and irrational numbers
Which of the following statements are true of irrational n umbers?
Check all that are true.
Repeating decimals are irrational numbers.
Irrational numbers can NOT be written as fractions.
The square root of two is an example of an irrational num ber.
In decimal form, irrational numbers continue on forever without ever repeating.
Irrational numbers can be written as one integer divided by another integer.
Question 1:
Which of the following statements are true of ratio nal numbers?
Check all that are true.
A repeating decimal is a rational number.
In decimal form, rational numbers continue on forever without ever repeating.
Rational numbers can NOT be written as fractions.
The square root of four is an example of a rational number.
A rational number can have zero as the denominator.
Question 2:
Which of the following statements are true of irrational n umbers?
Check all that are true.
Decimals that can be written as fractions are irrational numbers.
In decimal form, irrational numbers continue on forever without ever repeating.
Irrational numbers can be written as one integer divided by another integer.
Question 3:
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Lesson: Estimating Irrational Numbers

Lesson Topic: Identify rational and irrational numbers

Which of the following statements are true of irrational numbers? Check all that are true. Repeating decimals are irrational numbers. Irrational numbers can NOT be written as fractions. The square root of two is an example of an irrational number. In decimal form, irrational numbers continue on forever without ever repeating. Irrational numbers can be written as one integer divided by another integer. Question 1: Which of the following statements are true of rational numbers? Check all that are true. A repeating decimal is a rational number. In decimal form, rational numbers continue on forever without ever repeating. Rational numbers can NOT be written as fractions. The square root of four is an example of a rational number. A rational number can have zero as the denominator. Question 2: Which of the following statements are true of irrational numbers? Check all that are true. Decimals that can be written as fractions are irrational numbers. In decimal form, irrational numbers continue on forever without ever repeating. Irrational numbers can be written as one integer divided by another integer. Question 3:

Pi (p) is an example of an irrational number. The square root of three is an example of an irrational number. Which of the following statements are true of rational numbers? Check all that are true. One divided by zero is an example of a rational number. In decimal form, rational numbers continue on forever without ever repeating. Rational numbers can be written as fractions. The square root of four is an example of a rational number. Pi (p) is an example of a rational number. Question 4: Which of the following statements are true of irrational numbers? Check all that are true. Decimals that repeat after 10 digits are irrational. The square root of three is an example of an irrational number. Repeating decimals are irrational numbers. The square root of two is an example of an irrational number. Irrational numbers can NOT be written as fractions. Question 5:

The following irrational number is shown on which number line? Question 4: The following irrational number is shown on which number line? Question 5:

Lesson Topic: Estimate irrational square roots with rational square roots

Evaluate: is _______ Greater than 8 and less than 9 Greater than 5 and less than 6 Less than 1 Greater than 3 and less than 4 Greater than 1 and less than 2 none of the above Question 1: Evaluate: is _______

Greater than 4 and less than 5 Greater than 6 and less than 7. 5 Greater than 5 and less than 6 none of the above Question 2: Evaluate: is _______ Question 3:

Greater than 4 and less than 5 Greater than 5 and less than 7 5 × 11 Greater than 7 and less than 8 Greater than 8 and less than 9 none of the above Evaluate: is _______ Greater than 8 and less than 9 Greater than 4 and less than 5 Greater than 7 and less than 8 Greater than 5 and less than 7 64 none of the above Question 4: Evaluate: is _______ Greater than 8 and less than 9 Greater than 2 and less than 3 Greater than 5 and less than 6

64 Question 5: