Scientific Theories Quick Check
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Question
What is the goal of a theory?(1 point)
Responses
to explain natural and physical phenomena
to explain natural and physical phenomena
to control the outcome of an experiment
to control the outcome of an experiment
to determine independent and dependent variables
to determine independent and dependent variables
to analyze data from an experiment
to explain natural and physical phenomena
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Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
The relationship between rational numbers and whole numbers is that all whole numbers are a subset of rational numbers, but not all rational numbers are whole numbers.
Whole numbers include all the positive integers (1, 2, 3, ...), as well as the number zero (0). Rational numbers, on the other hand, include both the whole numbers and fractions or decimals that can be expressed as the ratio of two integers.
Examples:
- The number 3 is a whole number and also a rational number because it can be written as 3/1.
- The number -2 is a whole number but not a rational number because it cannot be expressed as a ratio of two integers.
- The fraction 1/2 is a rational number but not a whole number.
- The decimal 0.75 is a rational number but not a whole number.
In summary, every whole number can be considered a rational number because it can be expressed as a fraction with a denominator of 1. However, not all rational numbers are whole numbers because they may have fractional or decimal components.