An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
-10 is an integer.
5 is an irrational number.
− 5. 6 is a rational number, but not an integer.
3 4 1 is a rational number, but not an integer.
π is an irrational number.
-10: Integer, 5 : Irrational number , − 5. 6 : Rational number (not integer) , 3 4 1 : Rational number (not integer) , π : Irrational number
Explanation
Problem Analysis We are given a list of numbers: -10, 5 , − 5. 6 , 3 4 1 , and π . We need to classify each number as either an integer, a rational number (but not an integer), or an irrational number. Let's analyze each number individually.
Classifying -10 -10 is a negative whole number. Integers include all whole numbers, both positive and negative, and zero. Therefore, -10 is an integer.
Classifying 5 5 is the square root of 5. Since 5 is not a perfect square (i.e., it's not the square of an integer), its square root is an irrational number. Irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal representations.
Classifying − 5. 6 − 5. 6 is a repeating decimal. Repeating decimals are rational numbers because they can be expressed as a fraction. In this case, − 5. 6 = − 5.666... = − 3 17 . Since it is not a whole number, it is not an integer.
Classifying 3 4 1 3 4 1 is a mixed number, which can be written as an improper fraction. 3 4 1 = 4 3 × 4 + 1 = 4 13 . This is a rational number because it can be expressed as a fraction. Since it is not a whole number, it is not an integer.
Classifying π π (pi) is a well-known irrational number. It is the ratio of a circle's circumference to its diameter and has a non-repeating, non-terminating decimal representation.
Final Answer Therefore, the classifications are:
-10: Integer
5 : Irrational number
− 5. 6 : Rational number, but not an integer
3 4 1 : Rational number, but not an integer
π : Irrational number
Examples
Understanding number classifications is crucial in many real-world applications. For example, engineers use rational numbers to design structures with precise measurements. Cryptographers rely on irrational numbers for generating secure encryption keys. Financial analysts use integers to track profits and losses, while scientists use irrational numbers like pi in various calculations, from determining the circumference of a circular pipe to calculating the trajectory of a rocket. Knowing the properties of different types of numbers allows professionals to make accurate calculations and informed decisions in their respective fields.
In an electric device with a current of 15.0 A over 30 seconds, approximately 2.81 x 10^21 electrons flow through it. This is calculated by first determining the total charge delivered and then dividing by the charge of a single electron. Hence, the amount of charge and number of electrons are closely connected through their respective formulas.
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