Explain the main differences among integers, rational numbers, real numbers, and irrational numbers. Integers are the natural numbers of (0, 1,2,3,4….)and the negative non zero numbers of (-1,-2,-3,-4….)and so forth. Integers are numbers without a fractional or decimal component. Example: 23, 5, and -567 are integers, 8.45, 5½, and √2 are not integers. Integers are any number that can be expressed as the ratio of two integers. All integers are rational because integers can be expressed as a ratio of itself (9= 9/1) Rational numbers (fractional numbers) are regarded as divisions of integers. All numbers that are written as non-repeating, non-terminating decimals are “irrational” Example: Sqrt(2) or PI “3.14159…” the rational and irrationals are two different number types. Real numbers include whole numbers, rational numbers, and irrational numbers. A real number can be positive or negative or zero.
How are these numbers used in everyday life? Real numbers, integers and rational/irrational numbers are used frequently in everyday life. Stock Market, buying gas, doing inventory, tipping your waiter at a restaurant, baking, school grades, tuning to a radio station and the list goes on and on.
How would you explain the use of each to someone who did not know about the differences? Real life examples are important in teaching someone who didn’t know anything about these numbers. Visuals, so the person can see how many numbers they use in their everyday life will really help them understand.