To which sets of real numbers does zero belong?(1 point)
natural numbers, integers, and rational numbers
natural numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
The correct answer is:
whole numbers, integers, and rational numbers
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
(1 point)
Responses
the area of one of the cube’s faces
the area of one of the cube’s faces
the surface area of the cube
the surface area of the cube
the diagonal of one of the cube’s faces
the diagonal of one of the cube’s faces
the volume of the cube
The correct answer is:
the diagonal of one of the cube’s faces
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?(1 point)
Responses
square root of 3
square root of 3
47
Start Fraction 4 over 7 End Fraction
234
2 Start Fraction 3 over 4 End Fraction
−3
The correct answer is:
47
Zero belongs to the set of natural numbers, integers, and rational numbers.
To determine the sets of real numbers that zero belongs to, we need to understand the definitions of the various number sets.
- Natural numbers (also known as counting numbers) are the positive integers starting from 1 and continuing indefinitely. They do not include zero: {1, 2, 3, 4, ...}
- Whole numbers include zero and all the natural numbers: {0, 1, 2, 3, ...}
- Integers consist of positive and negative whole numbers, including zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}
- Rational numbers are any numbers that can be expressed as a fraction p/q, where p and q are integers, and q is not zero. This includes integers, since they can be expressed as a fraction with a denominator of 1. Rational numbers can be positive, negative, or zero.
- Irrational numbers are numbers that cannot be expressed as a simple fraction. They cannot be written as a terminating or repeating decimal. Examples include √2, π (pi), and e. Irrational numbers can be positive, negative, or zero.
Based on these definitions, the correct answer is:
Zero belongs to the sets of real numbers: whole numbers, integers, and rational numbers.
So, the first option is correct: natural numbers, integers, and rational numbers.