Explain the relationships and differences among real numbers, rational numbers, and irrational numbers.

The relationships and differences among real numbers, rational numbers, and irrational numbers.
Answer to Problem 1FCCE
Solution:
Relationship among real numbers, rational numbers, and irrational numbers is that the sets of rational numbers and irrational numbers are subsets of set of real numbers.
Difference between rational and irrational number is that the rational number can be written as
Explanation of Solution
Given information:
Set of real numbers, rational numbers, and irrational numbers
Explanation:
Rational numbers are the numbers which can be written as
Irrational numbers are the numbers which cannot be written as a ratio of two integers and have non-repeating and non-terminating decimals. For example,
The rational as well as irrational numbers can be converted to decimals and can be shown on the number line as shown below,
So, rational and irrational numbers are subsets of real numbers.
Want to see more full solutions like this?
Chapter 0 Solutions
Calculus & Its Applications
Additional Math Textbook Solutions
Pathways To Math Literacy (looseleaf)
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
APPLIED STAT.IN BUS.+ECONOMICS
Elementary Statistics: Picturing the World (7th Edition)
- 2. Find a matrix A with the following qualities a. A is 3 x 3. b. The matrix A is not lower triangular and is not upper triangular. c. At least one value in each row is not a 1, 2,-1, -2, or 0 d. A is invertible.arrow_forwardFind the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)arrow_forwardA 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.arrow_forward
- Explain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.arrow_forwarduse Cauchy Mean-Value Theorem to derive Corollary 12.6.2, and then derive 12.6.3arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning





