1. notation in both ascending and descending order.
Today’s lesson . . .
ascending
descending
What:
ORDERING RATIONAL NUMBERS
Why:
To order groups of fractions, decimals, percentages, and #’s written in scientific
notation in both ascending and descending order.

2. Start with the whole #’s, move onto the tenths, etc.
STRATEGY:
Start with the whole #’s, move onto the tenths, etc.
REVIEW (ORDERING DECIMALS):
When comparing decimal #’s, start with
the __________________________ place value
digit and compare. If there is a “tie,” move
on to the next digit, etc. In other words . . .
Compare the whole numbers.
If there is a “tie,” move on to the
______________________________ .
If there is another “tie,” move on to the
_______________________________.
If needed, keep moving on to the next
place value digit(s).
greatest
tenths
hundredths

3. Examples:
Put the following decimal numbers in ascending order: 1)
1.025
1.25
0.039
0.4
Answer: 2)
0.0055
0.2
0.015
0.15 3)
0.75
0.425
0.9
0.45
0.039; 0.4; ; 1.25
0.0055; ; 0.15; 0.2
0.425 ; 0.45; 0.75; 0.9

4. STRATEGY: Convert everything into decimals first!
Put the following numbers in ascending (least to
great) order: #
Frac.
Decimal %
Scientific Notation
Answer
(List in Original Form): 1.
1/8
0.0255
13%
1.25 x 10-2 2. 1¾
1.755
1.7%
1.7 x 103
1.25 x 10-2
0.0255
1/8
13%
Decimal
Version
0.017
1 ¾
1.755
1.7 x 103

5. Place the decimals from #3 (above) on the below number line:
On Your own: 3.
0.3
20%
2.5 x 10-3
2.5 x 10-3
20%
0.3
Place the decimals from #3 (above) on the
below number line:
0.0025
0.25
0.2
0.3
Hmmm. I wonder how
this number line
is divided??
Tenths of course!!

6. (List in Original Form):
Put the following numbers in descending (greatest
to least) order: #
Frac.
Decimal %
Scientific Notation
Answer
(List in Original Form): 1.
2/5
0.45
40.5%
4.1 x 10 -4 2.
2/3
0.6
66%
6.6 x 10-3
0.45
40.5%
2/5
4.1 x 10-4
2/3
66%
0.6
6.6 x 10-3
Place the decimals from #1 (above) on the below
number line:

7. Cynthia ran the least distance because
Word Problems: 1.
Amanda, Bill, Cynthia, and Max went running. Amanda ran 3.2 miles, Bill ran 3 2/5 miles, Cynthia ran 3.2 x miles, and Max ran 50% of 6 miles. Who ran the least amount of distance?
Cynthia ran the least distance because
She only ran miles, which is only
3.2% of a mile!

8. 2.
At Simpson Middle School, the 6th graders are absent 1/8 of the time,
the 7th graders are absent of
the time, and 8th graders are
absent 13.5% of the time. Which grade is absent the most?
The 8th graders are absent the most!

9. END OF LESSON
The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

10. Start with the whole #’s, move onto the tenths, etc.
Math-7 NOTES
DATE: ______/_______/_______
What: ORDERING RATIONAL NUMBERS
Why: To order groups of fractions, decimals, %’s, and #’s written in scientific
notation in both ascending and descending order.
NAME:
STRATEGY:
Start with the whole #’s, move onto the tenths, etc.
ascending
descending
REVIEW (ORDERING DECIMALS):
When comparing decimal #’s, start with the __________________________
place value digit and compare. If there is a “tie,” move on to
the next digit, etc. In other words . . .
Compare the whole numbers.
If there is a “tie,” move on to the ______________________________ .
If there is another “tie,” move on to the ___________________________.
If needed, keep moving on to the next place value digit(s).
Examples:
Put the following decimal numbers in ascending order: 1)
1.025
1.25
0.039
0.4
Answer: 2)
0.0055
0.2
0.015
0.15 3)
0.75
0.425
0.9
0.45

11. STRATEGY: Convert everything into decimals first!
Put the following numbers in ascending (least to great) order: #
Fraction
Decimal %
Scientific Notation
Answer
(List in Original Form): 1.
1/8
0.0255
13%
1.25 x 10-2 2. 1¾
1.755
1.7%
1.7 x 103 3.
0.3
20%
2.5 x 10-3
Decimal
Version
Place the decimals from #3 (above) on the below number line:

12. (List in Original Form):
Put the following numbers in descending (greatest to least) order: #
Fraction
Decimal %
Scientific Notation
Answer
(List in Original Form): 1.
2/5
0.45
40.5%
4.1 x 10 -4 2.
2/3
0.6
66%
6.6 x 10-3
Decimal
Version
Place the decimals from #1 (above) on the below number line:
Word Problems:
Amanda, Bill, Cynthia, and Max went running. Amanda ran miles,
Bill ran 3 2/5 miles, Cynthia ran 3.2 x 10-2 miles, and Max ran 50% of 6
miles. Who ran the least amount of distance?
At Simpson Middle School, the 6th graders are absent 1/8 of the time,
the 7th graders are absent 0.1 of the time, and 8th graders are absent
13.5% of the time. Which grade is absent the most?

13. (List in Original Form): (List in Original Form):
PRACTICE WORK
NAME:________________________________________________________________________________DATE: _____/_____/__________
“Ordering rational numbers”
Order the following from least to greatest (ascending): #
Fraction
Decimal %
Scientific Notation
Answer
(List in Original Form): 1.
4/5
0.08
80.5%
8 x 10 -3 2.
1/3
0.34
33%
3.3 x 10-2 3.
41/4
4.3
42.5%
4.25 x 102
Order the following from to greatest to least (descending): #
Fraction
Decimal %
Scientific Notation
Answer
(List in Original Form): 4.
0.025 2%
2.5 x 10-4 5.
5/6
0.83
8.3%
8.35 x 10-2 6.
14/16
0.0975
8.75%
8.75 x 102

14. “Ordering rational numbers”
PRACTICE WORK
NAME:________________________________________________________________________________DATE: _____/_____/__________
“Ordering rational numbers”