The diagram represents the relationship of number sets. The four choices given will complete the diagram. Which BEST describes the set of numbers in block A?
A: 5/3, 0.63, 0.0012
a integers
b whole numbers
c natural numbers
d rational numbers
d rational numbers
The set of numbers in block A consists of 5/3, 0.63, and 0.0012. To determine which choice best describes this set, let's analyze the properties of each option:
a) Integers: Integers are whole numbers and their negatives, including zero. However, the numbers in block A are not whole numbers, so this option is not the best choice.
b) Whole numbers: Whole numbers are integers that are greater than or equal to zero. Since the numbers in block A are not whole numbers, this option is also not the best choice.
c) Natural numbers: Natural numbers are positive integers greater than zero. Since the numbers in block A include a fraction and decimal, they are not natural numbers. Therefore, this option is not the best choice.
d) Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers, and the denominator is not zero. The numbers in block A, 5/3, 0.63, and 0.0012, are all rational numbers since they can be expressed as fractions. Therefore, the best choice to describe the set of numbers in block A is D: rational numbers.
To determine the set of numbers in block A, we first need to understand the definitions of the given number sets: integers, whole numbers, natural numbers, and rational numbers.
1. Integers: Integers are the set of positive and negative whole numbers, including zero. They do not include fractions or decimals.
2. Whole numbers: Whole numbers are similar to integers, but they do not include negative numbers. Whole numbers consist of zero and positive integers.
3. Natural numbers: Natural numbers are also known as counting numbers. They include all positive integers, starting from 1 and going up infinitely. Natural numbers do not include zero or negative numbers.
4. Rational numbers: Rational numbers are numbers that can be expressed as a ratio or fraction of two integers. They can be written in the form p/q, where p and q are integers, and q is not equal to zero. Rational numbers include integers, whole numbers, and fractions.
Looking at the given numbers: 5/3, 0.63, and 0.0012, we can observe that they are all fractions or decimals.
Out of the four options provided (integers, whole numbers, natural numbers, and rational numbers), the BEST description for the set of numbers in block A would be rational numbers (option d). This is because all the given numbers can be expressed as fractions.