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Consider the following set of real numbers: √2, -3/5, 1, 1.3Ì…, √5, 2.9. Which of the following lists all of the rational numbers in the set?

1) √2, -3/5, 1
2) -3/5, 1, 1.3Ì…
3) √2, 1, √5
4) -3/5, 1, 2.9

User Thiagoh
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1 Answer

4 votes

Final answer:

Option 2 is correct. It includes -3/5, 1, 1.3Ì, and 2.9, which can all be expressed as fractions, making them rational numbers. The other numbers from the list, √2 and √5, are irrational.

Step-by-step explanation:

The question asks us to identify the rational numbers in a given set of real numbers, which includes √2, -3/5, 1, 1.3Ì, √5, 2.9. A rational number can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Therefore, we need to determine which numbers can be expressed in such a format.

  • √2 and √5 are irrational numbers because they cannot be expressed as a simple fraction.
  • -3/5 and 1 are rational numbers, as they can be written as fractions (1 can be expressed as 1/1).
  • 1.3Ì (where the ellipsis Ì indicates a repeating decimal) is also a rational number, since repeating decimals can be converted into fractions.
  • 2.9 is a rational number because it is a terminating decimal and can be represented as 29/10.

From the list of options provided, the set that includes all rational numbers is option 2: -3/5, 1, 1.3Ì, 2.9.

User Pradeep Kashyap
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