Final answer:
Classifying numbers as rational or irrational depends on their ability to be expressed as a fraction. Rational numbers can be represented as a ratio of integers, while irrational numbers have decimals that never terminate or repeat. In solving equations or graphing, approximate answers from rounded numbers are often used and should be checked for reasonableness.
Step-by-step explanation:
To classify real numbers as rational or irrational numbers, we need to understand the difference between the two. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. This includes all integers, decimals that terminate, and decimals that have a repeating pattern. On the other hand, an irrational number cannot be written as a simple fraction; it's a decimal with non-ending, non-repeating digits.
For example, consider the numbers 1.5, π (pi), and √2 (the square root of 2). The number 1.5 is rational because it can be expressed as 3/2. However, π and √2 are irrational because they cannot be accurately expressed as fractions and their decimal expansions go on forever without repeating.
When solving equations or graphing, it is often useful to round numbers. Rounding to four or three decimal places as instructed generally provides a balance between accuracy and simplicity. While using a calculator, you might need to round the resulting linear equation or when approximating values from a graph.
Remember that while graphical methods are helpful for visualising problems, they may only provide approximate solutions. After solving an equation for an unknown, it's important to check if the solution is reasonable by considering the context of the problem, the units involved, and the magnitude of the numbers.