Question
Which set of numbers is always rational?(1 point)
Responses
fractions
fractions
decimals
decimals
integers
integers
positive numbers
bot, i believe its positive numbers.
Actually, that is incorrect. The correct answer is fractions. Fractions are always rational numbers, as they can be expressed as the quotient of two integers. Decimals can be rational or irrational, depending on whether they repeat or terminate. Integers are also rational numbers since they can be expressed as fractions with a denominator of 1. And positive numbers can be rational or irrational.
Actually, the set of numbers that is always rational is fractions. Rational numbers can be expressed as a fraction of two integers, where the denominator is not zero. Fractions include both positive and negative numbers, integers, and decimals, as long as they can be expressed as a ratio of two integers. So the correct answer is fractions.
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 fraction, where the numerator and denominator are both integers, and the denominator is not zero.
Let's go through each set of numbers and see if they fit the definition of rational numbers:
1. Fractions: Fractions are indeed rational numbers since they can always be expressed as a ratio of two integers, where the denominator is not zero. So, fractions are always rational.
2. Decimals: Decimals can be rational or irrational. Rational decimals are ones that terminate or repeat after a finite number of digits, like 0.5 or 0.333... (with 3 repeating). On the other hand, irrational decimals cannot be expressed as a fraction and do not terminate or repeat, like π (pi) or √2 (square root of 2). Therefore, while some decimals are rational, not all decimals are rational.
3. Integers: Integers are whole numbers without any fractional or decimal parts. They can be expressed as fractions by setting the denominator to 1. For example, the integer 5 can be expressed as 5/1. So, integers are also rational numbers.
4. Positive numbers: Positive numbers include both rational and irrational numbers. It is important to note that not all positive numbers are rational. For example, the square root of 2 (√2) is a positive irrational number. So, positive numbers cannot be considered as always rational.
Now, considering the above explanations and definitions, it is clear that the set of numbers that is always rational is fractions. So, the correct answer is "fractions."