9.486832981 is it rational or irrational

lucas.M

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22-01-2025

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The question of whether 9.486832981 is rational or irrational hinges on the definition of these terms. Let's explore this concept and then apply it to the given number.

Understanding Rational and Irrational Numbers

Rational numbers are numbers that can be expressed as a fraction p/q, where both p and q are integers, and q is not zero. These numbers can be precisely represented as terminating or repeating decimals. Think of fractions like 1/2 (0.5), 3/4 (0.75), or 1/3 (0.333...).

Irrational numbers, on the other hand, cannot be expressed as a simple fraction. Their decimal representations are non-terminating and non-repeating. Famous examples include π (pi) and the square root of 2. These numbers go on forever without any pattern in their digits.

Analyzing 9.486832981

The number 9.486832981 is a terminating decimal. This means its decimal representation ends. It doesn't continue infinitely with a repeating pattern or without any pattern at all.

Because it's a terminating decimal, it can be written as a fraction. While finding the exact fraction might require some manipulation, the possibility of expressing it as a fraction is key.

How to express 9.486832981 as a fraction:

1. Remove the decimal point: This gives us 9486832981.
2. Determine the denominator: The decimal has 9 places after the decimal point, so the denominator is 1 followed by nine zeros (1,000,000,000).
3. Form the fraction: The fraction is 9486832981/1000000000.

Since we've successfully expressed 9.486832981 as a fraction where both the numerator and denominator are integers, we can definitively conclude:

Conclusion: 9.486832981 is Rational

9.486832981 is a rational number. Its terminating decimal representation allows for its expression as a simple fraction, fulfilling the definition of a rational number. The fact that it's a relatively long decimal doesn't change its classification.