10 Questions
Which of the following statements is true about irrational numbers?
They have a decimal expansion that does not repeat or terminate.
What does it mean for a decimal expansion to repeat eventually?
The decimal digits repeat in a predictable pattern.
What is the relationship between rational and irrational numbers?
Rational and irrational numbers are mutually exclusive.
What is the approximate value of $\pi^2$?
6.28
How can rational approximations of irrational numbers be used to compare their sizes?
By finding rational numbers that are greater or smaller than the irrational numbers.
Which of the following is an example of a negative exponent?
4^-2
What does a negative exponent indicate?
Division
Which of the following is the reciprocal of 3^2?
1/9
What is the value of 2^-3?
1/8
If a number is raised to a negative exponent, what operation is involved?
Division
Study Notes
Irrational Numbers
- An irrational number is a real number that cannot be expressed as a finite decimal or fraction
- Irrational numbers have infinite non-repeating decimal expansions
Rational and Irrational Numbers
- Rational numbers are a subset of real numbers that can be expressed as a finite decimal or fraction
- Irrational numbers and rational numbers are mutually exclusive, but together they make up the set of real numbers
Decimal Expansions
- A decimal expansion that repeats eventually is a characteristic of rational numbers
- Irrational numbers have unique, non-repeating decimal expansions that go on indefinitely
Pi (π)
- π is an irrational number, approximately equal to 3.14
- The approximate value of π² is 9.86
Exponents
- A negative exponent indicates the reciprocal of the number
- For example, 2⁻³ is equal to 1/2³, or 1/8
- A negative exponent indicates that the operation involved is a reciprocal or "one over" the number
- 3⁻² is an example of a negative exponent, indicating 1/3² or 1/9
Comparing Irrational Numbers
- Rational approximations of irrational numbers can be used to compare their sizes
- By finding rational numbers close to the irrational numbers, comparisons can be made between them
Test your knowledge of Grade 8 Common Core Standards with this quiz! Explore the Number System and learn about rational and irrational numbers.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
