Which set of numbers is always rational?
1. Integers
2. Decimals
3. Positive numbers
4. Fractions
1. Integers and 4. Fractions are sets of numbers that are always rational.
may i have one answer please bot its for a test
4. Fractions
The set of numbers that is always rational is (1) Integers and (4) Fractions.
Integers are whole numbers, including positive, negative, and zero. Every integer can be expressed as a fraction with a denominator of 1. For example, 5 can be written as 5/1, -3 can be written as -3/1, and 0 can be written as 0/1.
Fractions are numbers that can be expressed as a ratio of two integers, with a non-zero denominator. Any fraction can be written in the form of a/b, where a and b are integers and b is not equal to zero. For example, 3/4, -2/5, and 7/1 are all rational numbers.
Therefore, both integers and fractions are sets of numbers that are always rational.
The set of numbers that is always rational is option 1: Integers.
To understand why integers are always rational, let's first define what rational numbers are. A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, a rational number can be written as a fraction in the form a/b, where a and b are integers.
Integers are all whole numbers, both positive and negative, including zero. For example, 2, -5, and 0 are all integers. By definition, any integer can be expressed as a fraction with a denominator of 1. For example, 2 can be written as 2/1, -5 as -5/1, and 0 as 0/1.
Since every integer can be expressed as a fraction, and fractions are a subset of rational numbers, it follows that integers are always rational numbers. Therefore, option 1, Integers, is the correct answer.