Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This includes integers, fractions, and finite or repeating decimals.
From the set provided:
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{3, -7, 1.25, 1/2, -3.2} - All numbers in this set are rational:
- 3 (an integer)
- -7 (an integer)
- 1.25 (can be expressed as 5/4, a fraction)
- 1/2 (a fraction)
- -3.2 (can be expressed as -32/10, a fraction)
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{3, -7} - Both numbers are integers, which are rational.
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{1.25, 1/2, -3.2} - 1.25 and -3.2 can be expressed as fractions, and 1/2 is already a fraction. All are rational.
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{3, -7, -3.2} - Includes integers and a decimal that can be expressed as a fraction.
From these evaluations, the entire first set {3, -7, 1.25, 1/2, -3.2} contains the most comprehensive list of rational numbers, and all options given contain rational numbers.
Thus, the rational numbers from the original set are:
- {3, -7, 1.25, 1/2, -3.2}.
If you need to select just one set from the options you’ve provided, you would choose {3, -7, 1.25, 1/2, -3.2} as it includes all the rational numbers listed.
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