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Finding which number supports the idea that the rational numbers are dense in the real numbers?

A. a fraction between π/2 and π/3
B. an integer between –11 and –10
C. a whole number between 1 and 2
D. a terminating decimal between –3.14 and –3.15

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Answer:

A terminating decimal between -3.14 and -3.15

Step-by-step explanation:

A natural number includes non-negative numbers like 5, 203, and 18476.

It is encapsulated by integers, which include negative numbers like -29, -4, and -198.

Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.

By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers)

Using the concept of dense numbers, it is found that the correct option is:

A. a fraction between π/2 and π/3

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  • The rational numbers are dense in the real numbers because all irrational numbers can be closely approximated to a rational.
  • There are no integers between -11 and -10, neither there are whole numbers between 1 and 2, thus, options B and C are incorrect.
  • Terminating decimals between -3.14 and -3.15, such as -3.141, are rational numbers, so it does not show the density, and thus, option D is incorrect.
  • [tex]\frac{\pi}{2}[/tex] and [tex]\frac{\pi}{3}[/tex], just as [tex]\pi[/tex], are non-terminating decimals, thus they are irrational numbers. However, through rounding, all can be approximated to a rational number, and thus, it shows that rational numbers are dense in the real numbers, being the correct option.

A similar problem is given at https://brainly.com/question/17405059

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