A. A number is a number that can be written as a fraction...

a. A _______ number is a number that can be written as a fraction whose numerator is an integer and whose denominator is a nonzero integer. b. All rational numbers can be expressed as terminating or ______ decimals. c. An _______ number is a number that cannot be expressed as a terminating decimal or as a repreating decimal. d. The set of _______ numbers includes the rational numbers and irrational numbers.

a. A _______ number is a number that can be written as a fraction whose numerator is an integer and whose denominator is a nonzero integer.
b. All rational numbers can be expressed as terminating or ______ decimals.
c. An _______ number is a number that cannot be expressed as a terminating decimal or as a repreating decimal.
d. The set of _______ numbers includes the rational numbers and irrational numbers.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rational Numbers

A rational number is a number that can be expressed as the quotient of two integers, with the denominator being nonzero. This concept provides the framework for understanding fractions and the underlying structure of the number system, as rational numbers can be represented either in fractional form or as a decimal that terminates or repeats.

Terminating and Repeating Decimals

Terminating decimals have a finite number of digits after the decimal point, while repeating decimals have a recurring sequence of digits. These decimal representations are fundamentally linked to rational numbers and illustrate the relationship between fraction formats and their decimal equivalents.

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as a simple fraction of two integers. Their decimal expansions are both non-terminating and non-repeating, distinguishing them from rational numbers. They play a critical role in expanding the number system to include values that fill the gaps along the number line.

Real Numbers

Real numbers consist of both rational and irrational numbers. This complete set of numbers covers every point on the number line and provides the basis for many areas of mathematics, including analysis and calculus, by ensuring that there are no 'gaps' within the continuum of numbers.

Transcript

Please give Ace some feedback