Podcast
Questions and Answers
Which statement accurately describes the decimal representation of rational numbers?
Which statement accurately describes the decimal representation of rational numbers?
- They terminate or repeat a fixed sequence of digits. (correct)
- They always terminate.
- They neither terminate nor repeat.
- They always repeat a fixed sequence of digits.
If a number's decimal expansion does not terminate and does not repeat, what type of number is it?
If a number's decimal expansion does not terminate and does not repeat, what type of number is it?
- An integer
- A rational number
- A real number
- An irrational number (correct)
Which of the following sets of numbers are all classified as rational?
Which of the following sets of numbers are all classified as rational?
- $\sqrt{2}$, $\pi$, 3.14159...
- $\sqrt{3}$, $\frac{1}{2}$, 0.666...
- $\frac{1}{3}$, 0, -5 (correct)
- $\pi$, e, $\sqrt{5}$
Which of the following statements is correct concerning the relationship between rational and real numbers?
Which of the following statements is correct concerning the relationship between rational and real numbers?
Consider a number x expressed as a fraction $\frac{a}{b}$, where a and b are integers. Under what condition is x NOT a rational number?
Consider a number x expressed as a fraction $\frac{a}{b}$, where a and b are integers. Under what condition is x NOT a rational number?
Flashcards
Rational Numbers
Rational Numbers
Numbers expressible as a ratio of two integers (p/q, q ≠0).
Forms of Rational Numbers
Forms of Rational Numbers
Fractions or decimals that either end or repeat a sequence.
Irrational Numbers
Irrational Numbers
Decimals that continue infinitely without repeating a pattern.
Integers as Rationals
Integers as Rationals
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Real Numbers
Real Numbers
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Study Notes
- Rational numbers can be expressed as a ratio of two integers.
- These numbers can be written as fractions or decimals.
- The decimal form of a rational number either ends or repeats a pattern of digits indefinitely.
- Decimals that neither terminate nor repeat represent irrational numbers.
- Integers, whether positive, negative, or zero, are also rational numbers.
- Together, rational and irrational numbers form the set of real numbers.
- The terms 'rational' and 'ratio' came into use independently, well after irrational numbers were identified by the Ancient Greeks.
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Description
Explore rational numbers, their expression as ratios or decimals, and their relation to integers and real numbers. Learn how rational numbers contrast with irrational numbers. Understand the historical context of the terms 'rational' and 'ratio'.
