"Students and faculty have to have this sense that they can truly connect with each other," he concludes. "Only through that sense of connection do you have this sense of community."
A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.
The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where
p and qare integers. Irrational, then, just means all the numbers that aren't rational.
Every integer is a rational number, since each integer
n canbe written in the form n/1.For example 5 = 5/1and thus 5 isa rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 arealso rational, since they are fractions whose numerator and denominator are integers.
So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on.
Is .999 repeating a rational number? Well, a number is rational if it can be written as A/B
(A over B): .3 = 3/10and .55555..... = 5/9,so these are both rational numbers. Now look at .99999999..... which is equal to 9/9 = 1.We have just written down 1 and .9999999 in the form A/B where A and B are both 9,so 1 and .9999999 are both rational numbers. In fact all repeating decimals like .575757575757... ,all integers like 46,and all finite decimals like .472are rational.