Today’s lesson . . .
What:
ORDERING RATIONAL NUMBERS
Why:
To order groups of fractions, decimals,
percentages, and #’s written in scientific
notation in both ascending and
descending order.
STRATEGY:
Start with the whole
#’s, move onto the
tenths, etc.
REVIEW (ORDERING DECIMALS):
When comparing decimal #’s, start with
greatest
the __________________________
place value
digit and compare. If there is a “tie,” move
on to the next digit, etc. In other words . . .
1) Compare the whole numbers.
2) If there is a “tie,” move on to the
tenths
______________________________
.
3) If there is another “tie,” move on to the
hundredths
_______________________________.
4) If needed, keep moving on to the next
place value digit(s).
Examples:
Put the following decimal numbers in
ascending order:
1.025
1.25
0.039
0.4
1)
Answer:
0.039; 0.4; 1.025; 1.25
0.0055
0.2
0.015
0.15
2)
Answer:
0.0055; 0.015; 0.15; 0.2
0.75
0.425
0.9
0.45
3)
Answer:
0.425 ; 0.45; 0.75; 0.9
STRATEGY: Convert
everything into
decimals first!
Put the following numbers in ascending (least to
great) order:
#
Frac.
1.
1/
8
Decimal
%
0.0255 13%
Scientific
Notation
Answer
(List in Original Form):
1.25 x 10-2
1) 1.25 x 10-2
2) 0.0255
Decimal
Version
3) 1/8
2.
4) 13%
1¾
1.755
1.7%
1.7 x 103
1) 0.017
2) 1 ¾
Decimal
Version
3) 1.755
4) 1.7 x 103
On Your own:
3.
¼
0.3
20%
2.5 x 10-3
1) 2.5 x 10-3
2) 20%
3) ¼
4) 0.3
Place the decimals from #3 (above) on the
below number line:
Tenths of
course!!
Put the following numbers in descending (greatest
to least) order:
#
Frac.
Decimal
1.
2/
5
0.45
%
Scientific
Notation
40.5% 4.1 x 10 -4
Answer
(List in Original Form):
1) 0.45
2) 40.5%
3) 2/5
4) 4.1 x 10-4
2.
2/
3
0.6
66%
6.6 x 10-3
1) 2/3
2) 66%
3) 0.6
4) 6.6 x 10-3
Place the decimals from #1 (above) on the below
number line:
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 10 -2 miles, and Max ran
50% of 6 miles. Who ran the least
amount of distance?
Cynthia ran the least distance because
She only ran 0.032 miles, which is only
3.2% of a mile!
2.
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?
The 8th graders are absent the most!
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.
Math-7 NOTES
NAME:
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.
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 . . .
1)
2)
3)
4)
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:
1.025
1)
0.4
0.2
0.015
0.15
0.425
0.9
0.45
Answer:
0.75
3)
0.039
Answer:
0.0055
2)
1.25
Answer:
STRATEGY:
Convert everything
into decimals first!
Put the following numbers in ascending (least to great) order:
Fraction
Decimal
%
Scientific
Notation
1.
1/
8
0.0255
13%
1.25 x 10-2
1¾
1.755
1.7%
1.7 x 103
¼
0.3
20%
2.5 x 10-3
Answer
(List in Original Form):
Decimal
Version
#
Decimal
Version
2.
Decimal
Version
3.
Place the decimals from #3 (above) on the below number line:
Put the following numbers in descending (greatest to least) order:
Fraction
Decimal
%
Scientific
Notation
1.
2/
5
0.45
40.5%
4.1 x 10 -4
2/
3
0.6
66%
6.6 x 10-3
Answer
(List in Original Form):
Decimal
Version
#
Decimal
Version
2.
Place the decimals from #1 (above) on the below number line:
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 10-2 miles, and Max ran 50% of 6
miles. Who ran the least amount of distance?
2.
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?
NAME:________________________________________________________________________________DATE: _____/_____/__________
PRACTICE WORK
“Ordering rational numbers”
Order the following from least to greatest (ascending):
#
Fraction
Decimal
%
Scientific
Notation
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
Answer
(List in Original Form):
Order the following from to greatest to least (descending):
#
Fraction
Decimal
%
Scientific
Notation
4.
¼
0.025
2%
2.5 x 10-4
5.
5/
0.83
8.3%
8.35 x 10-2
6.
14/
0.0975
8.75%
8.75 x 102
6
16
Answer
(List in Original Form):
NAME:________________________________________________________________________________DATE: _____/_____/__________
PRACTICE WORK
“Ordering rational numbers”