Indicate whether the following statement is True or False.
The number –3 is an integer and a rational number.
True
Which statement is false?
1. Every integer is a real number.
2. The number zero is a rational number.
3. Every irrational number is a real number.
4. Every real number is a rational number.
Statement 4 is false.
Which statement is true?
1.All irrational numbers are also rational numbers.
2.Half of the irrational numbers are also rational numbers.
3.One-third of the irrational numbers are also rational numbers.
4.Irrational numbers cannot be classified as rational numbers.
Statement 4 is true. Irrational numbers cannot be classified as rational numbers.
True.
The number -3 is an integer because it is a whole number that can be negative. An integer is any number that does not have a fractional or decimal part.
The number -3 is also a rational number because it can be expressed as a fraction, specifically -3/1. A rational number is any number that can be expressed as the ratio of two integers.
To determine whether the statement is true or false, we need to understand the definitions of an integer and a rational number.
An integer is a number that can be written without a fractional or decimal component. It includes positive numbers, negative numbers, and zero. Examples of integers are -3, -2, -1, 0, 1, 2, 3, etc.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Rational numbers can be written as fractions or decimals that either terminate or repeat. Examples of rational numbers are 1/2, -3/4, 0.25, -1.333, etc.
Now, let's analyze the statement:
"The number -3 is an integer and a rational number."
According to our definitions, -3 is indeed an integer since it is a negative whole number. However, is it also a rational number?
Yes, -3 can be expressed as the fraction -3/1, where the numerator (-3) and the denominator (1) are both integers. Therefore, -3 is a rational number.
So, the statement "The number –3 is an integer and a rational number" is true.
In summary, -3 is both an integer and a rational number.