Is the number 81 Irrational?
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Gabriel Hughes
Works at Amazon, Lives in Seattle. Graduated from University of Washington with a degree in Business Administration.
As a mathematical expert, I can provide a comprehensive explanation regarding the nature of the number 81 and its classification within the realm of numbers. To begin with, let's define what an irrational number is. An irrational number is a real number that cannot be expressed as a ratio of two integers, which means it cannot be written in the form \( a/b \) where \( a \) and \( b \) are integers and \( b \neq 0 \). Irrational numbers have decimal expansions that are non-repeating and infinite.
Now, let's consider the number 81. It is a positive integer, and it is a perfect square, as it is the square of 9 (\( 81 = 9^2 \)). One of the key characteristics of integers, especially those that are perfect squares, is that they can indeed be expressed as the ratio of two integers. Specifically, 81 can be expressed as \( 81/1 \), which is a simplified form of the ratio where both the numerator and the denominator are integers and the denominator is not zero.
The statement provided suggests that 81 is not irrational because it can be expressed as the quotient of two integers: \( 81/1 \). This is correct. Since 81 can be written in the form \( a/b \) where \( a = 81 \) and \( b = 1 \), it satisfies the condition for being a rational number. Rational numbers include all integers, fractions, finite decimals, and repeating decimals because they can all be expressed as a ratio of two integers.
It's important to note that the definition of irrational numbers is not just about being non-integers, but specifically about being non-repeating, non-terminating decimals that cannot be expressed as a simple fraction. Examples of irrational numbers include the mathematical constants π (pi), e (Euler's number), the square root of any non-perfect square, and most numbers involving roots or trigonometric functions that do not result in a perfect square or integer.
To summarize, the number 81 is a rational number because it meets the criteria for being expressible as a ratio of two integers. It is not an irrational number, which would require it to have a decimal expansion that is infinite and non-repeating, and cannot be simplified to a fraction of two integers.
Now, let's proceed with the translation as requested:
Now, let's consider the number 81. It is a positive integer, and it is a perfect square, as it is the square of 9 (\( 81 = 9^2 \)). One of the key characteristics of integers, especially those that are perfect squares, is that they can indeed be expressed as the ratio of two integers. Specifically, 81 can be expressed as \( 81/1 \), which is a simplified form of the ratio where both the numerator and the denominator are integers and the denominator is not zero.
The statement provided suggests that 81 is not irrational because it can be expressed as the quotient of two integers: \( 81/1 \). This is correct. Since 81 can be written in the form \( a/b \) where \( a = 81 \) and \( b = 1 \), it satisfies the condition for being a rational number. Rational numbers include all integers, fractions, finite decimals, and repeating decimals because they can all be expressed as a ratio of two integers.
It's important to note that the definition of irrational numbers is not just about being non-integers, but specifically about being non-repeating, non-terminating decimals that cannot be expressed as a simple fraction. Examples of irrational numbers include the mathematical constants π (pi), e (Euler's number), the square root of any non-perfect square, and most numbers involving roots or trigonometric functions that do not result in a perfect square or integer.
To summarize, the number 81 is a rational number because it meets the criteria for being expressible as a ratio of two integers. It is not an irrational number, which would require it to have a decimal expansion that is infinite and non-repeating, and cannot be simplified to a fraction of two integers.
Now, let's proceed with the translation as requested:
2024-05-12 22:50:34
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Works at the International Labour Organization, Lives in Geneva, Switzerland.
Answer : 81 is not an Irrational number because it can be expressed as the quotient of two integers: 81-- 1.
2023-06-15 02:45:04
Noah Thompson
QuesHub.com delivers expert answers and knowledge to you.
Answer : 81 is not an Irrational number because it can be expressed as the quotient of two integers: 81-- 1.
