Multiply And Divide With Scientific Notation Worksheet Page 3
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10The Density Property
Mississippi Standard:
Develop a logical argument to demonstrate the
‘denseness’ of rational numbers.
Examine the number line below. Find another integer that lies between the
integers
2 and 3.
-2 -1
0
1
2
3
4
The integers
1, 0, 1, and 2 all lie between
2 and 3 on the number line.
On the number line above, find a number that lies between 1 and 2. Their
1
average, 1
, is one number that lies between 1 and 2.
2
Find a Number Between Two Given Numbers
1
1
Find a number that lies between
and
on the number line below.
3
2
1
1
1
2
5
0
1
6
3
2
3
6
One number would be their average.
1
1
1
1
2
3
1
1
Rewrite
and
with a common denominator.
2
3
2
2
6
6
3
2
1
5
Add the numerators.
2
6
5
Multiply.
1
2
5
1
1
The rational number,
, lies between
and
.
1
2
3
2
Find a number that lies between
7 and
6.5.
One number would be their average.
1
1
[ 7
( 6.5) ]
( 13.5)
Add
7 and
6.5.
2
2
6.75
Multiply.
The rational number,
6.75, lies between
7 and
6.5.
The process above of finding another number between any two given numbers
can be continued indefinitely. This suggests the
.
density property
Density Property for Rational Numbers
Words
Between every pair of distinct rational numbers, there are infinitely
many rational numbers.
You can use the density property to solve real-world problems.
602
Prerequisite Skills
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