The Correct Answer and Explanation is:
The correct rational numbers from the list are:
0, 1.8125, √4, 29/8, and 8.429
Explanation:
A rational number is any number that can be written as a fraction a/b, where a and b are integers and b is not zero. This includes all terminating decimals, repeating decimals, integers, and proper fractions.
0 qualifies as rational because it can be written as 0/1, which fits the definition.
1.8125 is a terminating decimal and can be expressed exactly as 18125/10000. This simplifies to a fraction of integers, confirming it is rational.
√4 equals 2, which is an integer. Since integers can be written in the form a/1, it is rational.
29/8 is already written as a ratio of two integers, so it is clearly rational.
8.429 is a terminating decimal. It can be converted to the fraction 8429/1000, which confirms its rationality.
On the other hand:
√13 is irrational. The square root of 13 cannot be simplified into a whole number or a fraction, and its decimal form is non-terminating and non-repeating.
29.04040004… appears to have a non-repeating pattern after the decimal, which disqualifies it from being a rational number.
3.14159… is an approximation of π (pi), a well-known irrational number. Its decimal representation goes on forever without repeating.
Identifying rational numbers is useful in algebra, measurement, and data analysis because rational numbers have predictable and well-behaved properties. They allow exact representations in calculations, which is crucial in many scientific and engineering applications. Understanding the characteristics of rational versus irrational numbers builds a strong foundation in number theory and mathematical reasoning.
