Questions and Answers
What is a rational number?
What is a repeating decimal?
Decimal form of a rational number.
What defines a terminating decimal?
A decimal where the repeating digit is zero.
What is a power in mathematics?
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What is the base in a power?
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What is an exponent?
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What is a monomial?
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What is scientific notation?
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What is the square root?
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What is a perfect square?
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What does the radical sign represent?
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What is a cube root?
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What is a perfect cube?
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What is an irrational number?
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What defines a real number?
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Study Notes
Rational Numbers
- Rational numbers can be represented as the ratio of two integers; the denominator cannot be zero.
- Includes all integers, fractions, mixed numbers, and percentages.
Types of Decimals
- Repeating decimals: Decimal representation of a rational number that has digits that repeat indefinitely.
- Terminating decimals: A decimal that ends or has a final digit, specifically where the repeating digit is zero.
Exponents and Powers
- A power is formed by multiplying a base by itself a certain number of times, indicated by an exponent.
- The base in a power denotes the number being multiplied, while the exponent indicates how many times the base is multiplied.
Monomials
- A monomial can be a number, a variable, or the product of numbers and variables.
Scientific Notation
- A method to express very large or very small numbers compactly, such as 5,500 being written as 5.5 x 10^3.
Roots
- Square root: The number that, when multiplied by itself, yields the original number; for example, the square root of 144 is 12.
- Cube root: The number that, when multiplied by itself three times, gives the original number; for example, the cube root of 64 is 4.
Perfect Squares and Cubes
- A perfect square is a rational number with an integer as its square root; for instance, 25 is a perfect square because its square root is 5.
- A perfect cube contains a whole number as its cube root; an example is 27, with a cube root of 3.
Additional Concepts
- Radical sign: A symbol used to represent the positive square root of a number.
- Irrational numbers: Numbers that cannot be expressed as a fraction of two integers, such as √2 or π.
- Real numbers: Comprises both rational and irrational numbers, forming the complete set of numbers used in mathematics.
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Description
Test your knowledge with these flashcards on real numbers from Course 3 Chapter 1. Learn about rational numbers, repeating decimals, and terminating decimals through quick definitions and examples. Perfect for students looking to reinforce their understanding of fundamental mathematical concepts.
