"Not integral" means that something is not made up of whole numbers or units. In other words, it cannot be expressed as a whole number or ratio of whole numbers.
An example of something that is not integral is a fraction or decimal number. For instance, 1/2 and 0.5 are not integral because they cannot be written as a whole number or ratio of whole numbers.
"Not rational" means that something cannot be expressed as a ratio of two integers, while "not integral" means that something cannot be expressed as a whole number. Therefore, something can be not integral but still be rational, such as the square root of 2.
Yes, something can be both not integral and not rational. For example, the number pi (π) cannot be expressed as a whole number or ratio of whole numbers, making it not integral. It also cannot be expressed as a ratio of two integers, making it not rational.
Understanding these concepts is important in science because many physical quantities, such as measurements and calculations, are not always whole numbers or ratios of whole numbers. By understanding "not integral" and "not rational," scientists can accurately represent and manipulate these quantities in their research and experiments.