Examkin

Soru

Zorluk: OrtaClassification of Numbers

Consider the following set of 8 numbers:

S={−7,0,π,227,169,50,2.5,0.45‾}S = \left\{ -7, 0, \pi, \frac{22}{7}, \sqrt{169}, \sqrt{50}, 2.5, 0.\overline{45} \right\}

Let:
P=P = the number of integers in SS
Q=Q = the number of rational numbers in SS
R=R = the number of irrational numbers in SS
T=T = the number of whole numbers in SS

Calculate the exact value of (Q×R)+(P×T)(Q \times R) + (P \times T).

Cevap: 18

Cevap

18
Based on mathematical definitions: P (integers) = 3 because -7, 0, and 13 are integers. Q (rationals) = 6 because it includes the 3 integers plus 22/7, 2.5, and 0.4545... R (irrationals) = 2 because it includes pi and sqrt(50). T (whole numbers) = 2 because it includes the non-negative integers 0 and 13. Plugging these into (Q * R) + (P * T) yields (6 * 2) + (3 * 2) = 18.

Adım Adım Çözüm

1
Evaluate and simplify each number in the set to determine its properties.
\sqrt{169} simplifies to exactly 13. The repeating decimal 0.\overline{45} can be written as a fraction (45/99).
Numbers must be evaluated in their simplest form to avoid misclassification.
2
Determine the value of P by counting the integers.
The integers are -7, 0, and 13. Therefore, P = 3.
Integers include positive numbers, negative numbers, and zero, with no decimal or fractional parts.
3
Determine the value of Q by counting the rational numbers.
The rational numbers are -7, 0, 22/7, 13, 2.5, and 0.\overline{45}. Therefore, Q = 6.
Rational numbers are any numbers that can be expressed as a ratio of two integers.
4
Determine the value of R by counting the irrational numbers.
The irrational numbers are \pi and \sqrt{50}. Therefore, R = 2.
Irrational numbers have non-terminating, non-repeating decimal expansions.
5
Determine the value of T by counting the whole numbers.
The whole numbers are 0 and 13. Therefore, T = 2.
Whole numbers consist only of the non-negative integers.
6
Substitute the counts into the requested mathematical expression and calculate the final result.
(6 \times 2) + (3 \times 2) = 12 + 6 = 18.
To answer the specific question given in the stem.

Anahtar Kavram

Classification of real numbers into integers, rational numbers, irrational numbers, and whole numbers.
Bu soruyu puanla

Konular

Classification of Numbers

Bu konudan daha fazla soru