Describe the set of numbers that are real numbers but cannot be expressed as one integer divides by another.
1.negative
2.improper
3.irrational
4.rational
Please help!
The set of numbers that are real numbers but cannot be expressed as one integer divides by another consists of:
1) Negative numbers: For example, -2 or -3 cannot be expressed as one integer divides by another since any positive integer divided by another positive integer will yield a positive result.
2) Improper fractions: These are fractions where the numerator is greater than or equal to the denominator. For example, 5/4 or 7/3 cannot be expressed as one integer divides by another since the result would be a proper fraction.
3) Irrational numbers: These are numbers that cannot be expressed as fractions and have non-repeating and non-terminating decimal representations. Examples include √2, π (pi), or e (Euler's number). These numbers cannot be expressed as one integer divides by another since they do not have a finite or repeating decimal representation.
4) Rational numbers: These are numbers that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero. Rational numbers can be expressed as one integer divides by another. Examples include 1/2, -3/4, or 5/1.
To which sets of real numbers does Zero belong?
1. natural numbers, integers, and irrational numbers
2. Whole numbers, integers, and rational numbers
3. Natural numbers, integers, and rational numbers
4. Whole numbers, integers, and irrational numbers
The correct answer is option 2: Zero belongs to the set of whole numbers, integers, and rational numbers.
1. Zero does not belong to the set of natural numbers because natural numbers do not include zero by definition.
2. Zero does belong to the set of whole numbers because whole numbers include zero and all non-negative integers.
3. Zero does belong to the set of integers because it is an integer.
4. Zero does belong to the set of rational numbers because it can be expressed as 0/1, which is a fraction of two integers.
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A cube has an edge length, a, that is a rational number of centimeters. Identify which measurement it Will require the use if irrational numbers.
1. The volume of the cube
2. The área of one of the cubes faces
3. The diagonal of one of the cubes faces
4. The Surface área of the cube
The measurement that will require the use of irrational numbers for a cube with edge length, a, that is a rational number of centimeters is:
3. The diagonal of one of the cube's faces
The diagonal of a square face of a cube can be found using the Pythagorean theorem, which involves the square root of the sum of the squares of the two sides. Since the edge length is rational, the diagonal length will most likely be an irrational number, as it involves taking the square root of a non-perfect square.
Which of the following numbers could be used to specify how Many cups of flour should be used in a bread recipe?
1. -3
2. Square root of 3
3. 2 3/4
4. 4/7
The number that could be used to specify how many cups of flour should be used in a bread recipe is:
3. 2 3/4
The measurement 2 3/4 represents a mixed number, and it is a valid quantity for specifying the amount of flour in cups for a bread recipe. It is a rational number and can be easily understood and measured accurately.
Option 1, -3, is a negative number that does not align with the concept of measuring a quantity of flour in cups.
Option 2, the square root of 3, is an irrational number that does not represent a specific quantity in cups.
Option 4, 4/7, is a rational number but it does not represent a clear and standard measurement like a whole number or a mixed number.