Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
Responses
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers - not selected, this is the correct answer
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers - no response given
natural numbers, whole numbers, integers, rational numbers
natural numbers, whole numbers, integers, rational numbers - incorrect
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi - incorrect
Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
rational numbers, integers, whole numbers, natural numbers
integers, rational numbers, natural numbers, whole numbers
natural numbers, whole numbers, integers, rational numbers
irrational numbers, square roots, endless decimals, pi
Please explain shortly
The correct hierarchy of number sets within the real number system, from largest to smallest, is:
rational numbers, integers, whole numbers, natural numbers.
Rational numbers include all numbers that can be expressed as a fraction or ratio of two integers.
Integers include both positive and negative whole numbers, including zero.
Whole numbers include all positive integers and zero.
Natural numbers include all positive integers, excluding zero.
The other options listed do not follow this correct hierarchy.
can you make it shorter
Sure! The correct hierarchy of number sets is:
Rational numbers > Integers > Whole numbers > Natural numbers.
Please explain shortly
To which sets of real numbers does zero belong?
Responses
whole numbers, integers, and irrational numbers
natural numbers, integers, and rational numbers
natural numbers, integers, and irrational numbers
whole numbers, integers, and rational numbers
Zero belongs to the sets of real numbers: whole numbers, integers, and rational numbers.
Explanation:
- Zero is included in the set of whole numbers as it is a non-negative integer, including zero itself.
- Zero is also included in the set of integers as it can be represented as 0/1, which is a ratio of two integers.
- Zero is part of the set of rational numbers as it can be expressed as a ratio of two integers (0/1).
Using a number line, what is the approximate value of 19−−√
4.25
4.13
4.5
4.38
Please explain shortly
The approximate value of √19 on a number line is 4.38.
Explanation:
To find the approximate value of √19 on a number line, we need to locate a value between which two integers the square root falls. When estimating, we know that 19 is closer to 16 (4²) than 25 (5²). So, we can estimate that √19 is slightly greater than 4. Therefore, the closest approximation is 4.38, which is closer to 4.38 than any of the other given options.
Please explain
Using rational approximations, what statement is true?
Responses
16 −−−√<4
12 −−−√<π
16−−√>4
12 −−−√ >π