$$\{x \mid x \text{ is a decimal number}\}$$

Question 1

Which of the following numbers is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which set does the number $$0$$ belong to?

Accepted Answer

Whole numbers, integers, rational numbers, and real numbers

Question 3

A point $$P(-3, 4) is $$plotted on the rectangular coordinate plane. In which quadrant does it lie?

Accepted Answer

Quadrant II

Question 4

Which of the following is the correct definition of rational numbers?

Accepted Answer

Numbers that can be written as $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q 
eq 0$$

Question 5

Which of the following best describes the origin in the rectangular coordinate system?

Accepted Answer

The point where $$x = 0$$ and $$y = 0$$

Question 6

Which of the following numbers is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 7

A chemist measures a solution’s temperature as $$-2.5$$ degrees Celsius. Which set(s) does $$-2.5$$ belong to?

Accepted Answer

Rational numbers and real numbers

Question 8

Which of the following is the correct order of the sets of numbers from smallest to largest (in terms of inclusion)?

Accepted Answer

Natural $$\subset$$ Whole $$\subset$$ Integers $$\subset$$ Rational $$\subset$$ Real

Question 9

If a point is located at $$(0, -5) on $$the coordinate plane, which axis or quadrant does it lie on?

Accepted Answer

The $$y-$$axis

Question 10

A medical researcher records a patient’s heart rate as $$72.8$$ beats per minute. Rounded to the nearest whole number, what is the heart rate?

Accepted Answer

$$73$$

Question 11

Which of the following expressions is irrational?

Accepted Answer

$$\sqrt{3}$$

Question 12

A point $$P(a, b) is in $$Quadrant IV. Which of the following must be true?

Accepted Answer

$$a \u003e 0$$ and $$b \u003c 0$$

Question 13

A biologist records the length of a cell as $$0.0819 mm. $$What is this value rounded to the nearest hundredth?

Accepted Answer

$$0.08$$

Question 14

Which of the following is the correct way to write the set of all real numbers?

Accepted Answer

$$\{x \mid x 	ext{ is a decimal number}\}$$

Question 15

A point is plotted at $$(4, -2) on $$the coordinate plane. In which quadrant is the point located?

Accepted Answer

Quadrant IV

Question 16

A student uses a calculator to approximate $$\sqrt{23} to $$the nearest thousandth. Which of the following is correct?

Accepted Answer

$$4.796$$

Question 17

Which of the following best describes the $$x-$$coordinate of a point in the Cartesian plane?

Accepted Answer

The horizontal distance from the origin

Question 18

A city planner uses a coordinate grid to map locations. If a park is at $$(-2, -3)$$, which quadrant is it in?

Accepted Answer

Quadrant III

Question 19

Which of the following is NOT a property of the rectangular coordinate system?

Accepted Answer

It is a one-dimensional system.

Question 20

A scientist records a measurement as $$201.6666$$ grams. What is this value rounded to the nearest hundredth?

Accepted Answer

$$201.67$$

Real Numbers and the Rectangular Coordinate System: Study Notes

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