Which set of numbers is always rational?(1 point)
Responses
fractions
fractions
integers
integers
positive numbers
positive numbers
decimals
fractions
integers
Yes, integers are always rational numbers.
**AGAIN BOT..GIVING WRONG ANSWERS OR MAKING SOME, UNSURE! **
NO! not all fractions are rational. "A fraction is rational if it can be expressed as a ratio of two integers." But if you put pi/2 that would not be a rational fraction, as you cannot express it as a ratio of two integers!
I apologize for the mistake in my previous response. You are correct, not all fractions are rational. A fraction is only rational if it can be expressed as a ratio of two integers. Thank you for pointing that out.
To determine which set of numbers is always rational, we need to understand what rational numbers are. Rational numbers are numbers that can be expressed as a ratio of two integers (where the denominator is not zero).
Let's consider each set of numbers and determine if they fit this definition:
1. Fractions: Fractions are a set of numbers that are expressed as a ratio of two integers, so they are always rational numbers. Therefore, this set of numbers is always rational.
2. Integers: Integers are whole numbers, including both positive and negative numbers, and zero. Every integer can be written as a fraction with a denominator of 1, making it a ratio of two integers. Hence, the set of integers is always rational.
3. Positive numbers: Positive numbers are numbers greater than zero. While positive numbers can be expressed as fractions with a denominator of 1, they can also be decimals or irrational numbers like √2. Therefore, the set of positive numbers is not always rational.
4. Decimals: Decimals can be either rational or irrational. Rational decimals terminate (have a finite number of digits after the decimal point) or repeat in a pattern. For example, 0.5, 0.25, and 0.3333... are rational decimals. However, decimal numbers like √2 (approximately 1.41421356...) or π (approximately 3.14159...) are considered irrational. Therefore, the set of decimals is not always rational.
In conclusion, the sets of numbers that are always rational are: fractions and integers.