Download PA_M6_S2_T2_Comparing Real Numbers Transcript - NTER

PA_M6_S2_T2_Comparing Real Numbers Transcript
Just like when we work with whole numbers and natural numbers, or
integers we often want to compare real numbers to see which one is
greater or smaller than the other one.
I want to remind you of some notation when we start this. The equal sign
means "equal to," it's identically equal to. What is on the left has
exactly the same value as what is on the right. If I put a dash across
this it says it's not equal to. So I can make the statement
, "0 is
not equal to 5," which has the English translation with all these words
in it. The symbol really makes it more efficient to write.
If I have these squiggly lines,
it means it "is approximately equal
to," so when I gave you
as an approximation, this is how you saw it
written.
An angle bracket that points to the left, <, is the "less than" symbol.
This is a strict inequality it means that everything to the left of the
number, but not including the number, is less than that number. A
"greater than", >, is also a strict inequality. This tells me that what's
on the left, at the fat end of my little pointing arrow, is larger than
what is on the right.
If I put a bar underneath it, , that means that my value could be "less
than or equal to" so that everything to the left, including the number
I'm talking about, may satisfy the inequality. So this is called an
"inclusion." "Greater than or equal to" , , is also an inclusion. It
tells me that what's on the left of the sign is larger than, or perhaps
equal to, what's on the right.
When I talk about my number lines, the convention is that as I move to
the left things are smaller, as I move to the right things are bigger. So
that, on a number line, if I plot the number here and I plot a number
somewhere over here, this number is less than this number and that's what
it means. It sits to the left, it's smaller.
This is
important to pay attention to when I have negative signs involved because
-4 < -3, while 4 > 3. I can write this as 3<4 or 4>3. Both of those are
equivalent statements.
Let's practice a few. Let's insert the correct symbol in these
expressions to make each statement true.
-2 and -12. -2 sits to the right of -12 on a number line, it is therefore
greater than -12. -2 > -12.
-3.42 and -3.51. We
have to look at this really carefully, but -3.51
will sit farther to the left than -3.42 so that 3.42 is actually larger than -3.51, -3.42 > -3.51.
Here's one, |-0.5| and |½|. |-0.5| and |½| both
have exactly the same absolute value. They both sit
the same distance away from 0. The absolute value
of these two real numbers is the same so this is an
"equals to" case. √ and √ . This is one where we
might want to plot it on our number line to make
sure we know which one sits to the left of the
other. We could also use estimation techniques if
we want to calculate these. √
2.828 if I take
it to three decimal places.
√
That tells me that
√
√
All I needed to do was look at the tenths place, in this case, to see
where was greater.
This is how I can compare and order real numbers using my inequality
notation.