Comparing & Connecting Rationals
- Return & discuss the Quiz
- Collect homework; will discuss on Tues.
- Handout exam review sheet
- Discuss Sec. 6.5
- Comparing , Connecting Rationals
Homework: Sec. 6.5
1, 4, 5, 7, 8, 9, 10, 21, 23, 27
Sec. 6.5 - Comparing & Connecting Rationals
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|How do we compare fractions with paper & pencil
If the denominators are the same ...
|The rational numbers have a denseness property
that a rational number can always be found between any two
rational numbers .
The study of rational numbers is the first time students work
with a set of numbers that is dense rather than discrete.
This means we should avoid statements like :
0.6 is the number right next to 0.5, or
3/5 is the fraction between 2/5 and 4/5
b) Find three rational numbers between 11/15 and 0.8.
|So we know the set of rational numbers is dense
("there exists a
rational number between any two rational numbers").
Does this imply...
a) That there are an infinitely many rationals between any two
rational numbers? Yes
|We have seen that every terminating or repeating
rational (i.e., it can be expressed as a ratio of two integers .)
Let's see how we can find these fraction representations ...
The easy case terminating decimals :
|The interesting case repeating decimals :