To which set of numbers does 13.274... belong? and Why?
A) whole
B) integer
C) rational
D) Irrational
not really knowing what your ... means it is either rational or irrational
if there is a repeating decimal, then rational
if there is no pattern to your decimals, then irrational
To determine which set 13.274... belongs to, let's analyze each option:
A) Whole numbers: Whole numbers are non-negative integers, which means they do not include decimal numbers or fractions. Since 13.274... is a decimal number, it does not belong to the set of whole numbers.
B) Integers: Integers are positive whole numbers, negative whole numbers, and zero. Similar to whole numbers, integers do not include decimal numbers or fractions. Therefore, 13.274... is not an integer.
C) Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. To determine whether 13.274... is rational, we need to check if it can be expressed as a fraction. As the decimal part of 13.274... continues indefinitely without repetition, it cannot be expressed as a finite or repeating fraction. Therefore, 13.274... is not a rational number.
D) Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction, and their decimal representation goes on infinitely without repeating. In this case, 13.274... cannot be expressed as a fraction, and its decimal representation goes on infinitely without repeating. Therefore, 13.274... is an irrational number.
Hence, the answer is D) Irrational.
To determine which set of numbers the decimal 13.274... belongs to, we need to understand the definitions of each set of numbers.
A) Whole numbers: Whole numbers are non-negative numbers that do not have any decimal or fractional parts. They include all positive integers and zero.
B) Integers: Integers are whole numbers that can also include negative numbers, along with zero.
C) Rational numbers: Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. They can be either terminating or repeating decimals.
D) Irrational numbers: Irrational numbers are numbers that cannot be represented as a fraction or ratio of two integers. They are non-repeating and non-terminating decimals.
To determine the set that 13.274... belongs to, we can examine its nature. The decimal 13.274... is non-terminating, meaning it continues indefinitely without repeating or ending. Since 13.274... cannot be expressed as a fraction or ratio of two integers, it falls into the category of irrational numbers.
Therefore, the correct answer is D) Irrational.