in this video we're going to talk about rational and irrational numbers so what is the difference between a rational and an irrational number what would you say well first what is a rational number a rational number is any number that be that can be written as a ratio of two integers for example a fraction like three over four is a rational number or negative seven over six these are rational numbers because you can write them as a ratio of two integers and remember integers are basically whole numbers natural numbers or even uh negative numbers like these these are all integers so here's a question for you is an integer a rational number or an irrational number for example the integer eight would you put it on the left column or on the right column so can we write eight as a ratio of two integers we can write eight as sixteen divided by two so eight is a rational number what about a negative number like a negative five is that a rational number negative five can be written as a ratio of two integers you can write it as negative ten divided by 2. so negative 5 is a rational number in fact all integers are rational numbers now what about let's say decimal numbers for instance 0.25 is that rational or irrational can we write this as a fraction using two integers point 25 is the same as 25 divided by 100 and if you divide the top and the bottom number by 25 this is the same as 1 over 4. so if you have a decimal number that is finite that comes to an end like 0.25 that's a rational number another example is point fifteen this you can write that as fifteen divided by a hundred and if you divide the top and the bottom numbers by five you could reduce that to three over twenty now what about repeating decimals for instance let's say if we have 0.6666 repeating which we can write as 0.6 with a line on top is that rational or irrational 0.6 repeating is 6 over 9 which you could reduce that to 2 over 3 if you divide by 3. so repeating decimals are irrational numbers another example is point two repeating this is two over nine now what about let's say point seventeen repeating is that a rational number in this case we can write it as a ratio of two integers point seventeen repeated is seventeen over ninety nine so whether you have a finite decimal number or one that goes on forever but repeats they're all rational numbers now what about square roots for instance the square root of 9 would you say it's rational or irrational the square root of 9 is 3 and 3 is an integer and all integers are rational numbers but now what about the square root of 7 is it rational or irrational we can't simplify the square root of 7 to a whole number so if you use a calculator you'll find that the square root of seven is two point six four five seven five one three one and this can go on for a long time so whenever you see a decimal number that is non-repeating and that goes on forever and if you can't write it as a fraction of two integers that's when you have an irrational number so one way to identify them is if you have a square root that can't be simplified to an integer typically that's an irrational number now what about pi is pi rational or irrational so if you type pi into your calculator you're going to get a decimal number that looks like this 3.14 159265 and this also goes on so pi is an irrational number another example is the number e if you get the decimal value for that it's 2.71828182 and so forth so that's how you can identify irrational numbers it's basically numbers with an infinite number of decimal places it goes on forever and you can't write it as a ratio of two integers and so that's basically it for this video now you know how to identify a rational number and an irrational number thanks again for watching and don't forget to subscribe to this channel