FRACTION AS RATIONAL NUMBERS HELP HOW TO
How to convert a repeating decimal into a fraction Do you believe we CAN write it as a fraction, in the form a/b? This sounds like it would be pure guesswork, but no, there is a method, a nice and clever one, in my opinion. In fact, every non-terminating decimal number that REPEATS a certain pattern of digits is a rational number. What do you get? How about 2/9? 3/9? 1/11? 2/13? 7/15? Can you find more fractions that turn into non-terminating decimal numbers? Take for example 1/9 and convert it into a decimal number with long division algorithm. How about non-terminating decimal numbers? You might have never heard of those, though I hope you have. We talked how terminating decimal numbers are obviously rational numbers. Non-terminating repeating decimals are rational The line y = Pi * x indeed looks like it goes through the point (7,22) since the graphics program cannot draw accurately enough. But since it goes close, 22/7 is a nice approximation to Pi. It really wouldn't go throuhg it if we could draw extremely accurately, it would just go close. Of course when you are drawing lines on paper or on computer, you are limited in your accuracy and even a line y = Pi*x probably to go through a point with whole number coordinates, namely the point (7,22). They just avoid touching any of the points with whole number coordinates, and their slope is an irrational number!!! Difficult to fathom. Now, can you imagine a line through origin that does NOT touch ANY of these points with whole number coordinates? It's hard, but those kind of lines do exist. Practice a little: What is the first point with whole-number coordinates that these lines go through?Ī) y = 9x b) y = 243x c) y = 5/6x d) y = 8/3 x e) y = 345/1039 x Also, the points I listed are the FIRST points with whole-number coordinates these lines go through (after the origin).
![fraction as rational numbers help fraction as rational numbers help](http://1.bp.blogspot.com/-Uabt_YZdt7Q/UTIlTvxUa4I/AAAAAAAAA9c/tFG45w3tt6E/s1600/Adding+SUbtracting+Fractions+Anchor+Chart.jpg)
![fraction as rational numbers help fraction as rational numbers help](https://i.pinimg.com/originals/4b/a6/f8/4ba6f82fd791b5dbfd474b3e39e7eeff.jpg)
Line y = (9/2) x goes through the point (2, 9).Īnd so on. Line y = (1/3) x goes through the point (3, 1). Line y = 5 x goes through the point (1, 5). We can illustrate positive rational numbers in the coordinate plane with lines that go through the origin and another point with whole number coordinates. Terminating decimal numbers can also easily be written in that form: for example 0.67 = 67/100, 3.40938 = 340938/100000, and so on. Clearly all fractions are of that form, so fractions are rational numbers. The definition says that a number is rational if you can write it in a form a/b where a and b are integers, and b is not zero.