The first thing that comes to mind when I think of “rational numbers” is that numbers can’t be rational or irrational, because there numbers. With that in mind lets take a look at what is actually meant by “rational number”. A rational number is the quotient of a pair of integers (a/b, b≠0) that can be represented by a fraction or a decimal. Let’s back up a second, a “quotient” is just the product of divisibility.
I’m a little confused now. Let’s take a look at this video explaining rational numbers.
Ok, so a rational number is any number that can be written as a fraction. Of course if there are rational numbers, there must be some that are irrational. We’ll cover irrational at a later date, but basically numbers like pi where there’s no end and no repeating after the decimal point. Examples of rational numbers are any fraction, any whole number, any mixed number and any decimal number that repeats or has a repeating pattern.
One thing that I don’t remember ever seeing in any math class I have taken is how to calculate how to find the fraction equivalent for a number with a repeating decimal. It’s really clever how it works and makes a lot of sense!
Lets start with r=0.22222….
10r=2.222222
-r=0.222222
9r=2.0
r=2/9
So the fraction would be 2/9
How about something a little more complicated
r=.24747
1000r=247.4747
-10r= - 2.4747
990r=245
r=245/990
r=49/198
As long as there is some sort of repetition after the decimal place, the number can be proven to be rational!
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