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- Writing Integers as Rational Numbers. Write each of the following as a rational number. ⓐ7 ⓑ0 ⓒ–8. Solution. Write a fraction with the integer in the numerator and 1 in the denominator.
- Identifying Rational Numbers. Write each of the following rational numbers as either a terminating or repeating decimal. ⓐ − 5 7 − 5 7. ⓑ 15 5 15 5.
- Differentiating Rational and Irrational Numbers. Determine whether each of the following numbers is rational or irrational. If it is rational, determine whether it is a terminating or repeating decimal.
- Classifying Real Numbers. Classify each number as either positive or negative and as either rational or irrational. Does the number lie to the left or the right of 0 on the number line?
- Classifying a Real Number. The numbers we use for counting, or enumerating items, are the natural numbers: \(1, 2, 3, 4, 5\) and so on. We describe them in set notation as \(\{1,2,3,...\}\)
- Irrational Numbers. At some point in the ancient past, someone discovered that not all numbers are rational numbers. A builder, for instance, may have found that the diagonal of a square with unit sides was not \(2\) or even \(32\), but was something else.
- Real Numbers. Given any number \(n\), we know that \(n\) is either rational or irrational. It cannot be both. The sets of rational and irrational numbers together make up the set of real numbers.
- Sets of Numbers as Subsets. Beginning with the natural numbers, we have expanded each set to form a larger set, meaning that there is a subset relationship between the sets of numbers we have encountered so far.
Feb 19, 2024 · Because of the evolution of the number system, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
Nov 14, 2022 · The real numbers can be visualized on a horizontal number line with an arbitrary point chosen as \(0\), with negative numbers to the left of \(0\) and positive numbers to the right of \(0\). A fixed unit distance is then used to mark off each integer (or other basic value) on either side of \(0\).
1.1 Real Numbers: Algebra Essentials. Learning Objectives. In this section, you will: Classify a real number as a natural, whole, integer, rational, or irrational number. Perform calculations using order of operations. Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity.
Classify a real number as a natural, whole, integer, rational, or irrational number. Perform calculations using order of operations. Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity. Evaluate algebraic expressions. Simplify algebraic expressions.
Topics covered in this section are: Classify a real number as a natural, whole, integer, rational, or irrational number. Perform calculations using order of operations. Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity. Evaluate algebraic expressions.
