Classifying Real Numbers

Front

What are real numbers?

Back

Real numbers include all the numbers on the number line, including rational numbers (like integers and fractions) and irrational numbers (like square roots of non-perfect squares).

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What is a rational number?

Back

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.

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What is an irrational number?

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An irrational number is a number that cannot be expressed as a simple fraction; its decimal representation goes on forever without repeating.

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What are natural numbers?

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Natural numbers are the set of positive integers starting from 1 (1, 2, 3, ...).

Front

What are integers?

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Integers are whole numbers that can be positive, negative, or zero (-2, -1, 0, 1, 2, ...).

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What is a repeating decimal?

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A repeating decimal is a decimal fraction that eventually repeats a sequence of digits (e.g., 0.333... or 0.142857142857...).

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What is a terminating decimal?

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A terminating decimal is a decimal that has a finite number of digits after the decimal point (e.g., 0.75 or 2.5).

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How do you convert a repeating decimal to a fraction?

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To convert a repeating decimal to a fraction, set the decimal equal to a variable, multiply to shift the decimal point, and then solve for the variable.

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What kind of decimals are irrational?

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Irrational decimals are those that never end and have no repeating pattern.

Front

What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as fractions, while irrational numbers cannot be expressed as fractions.