Transcript Comparing and Ordering Decimals

Comparing and Ordering
Decimals
Objective
• Learn to write, compare, and order
decimals using place value and
number lines.
Menu Activity
• What is the most expensive item on the menu?
– 1 Dozen Pepperoni Rolls at $12.99
• What is the least expensive item on the menu?
– Small beverage at $0.69
• 1 large 14” Cheese Pizza is $5.99
– What item is more expensive?
• 1 large 14” Supreme Pizza ($8.99), 1 Dozen Pepperoni Rolls ($12.99)
– What item is less expensive?
• 8 Chicken wings ($5.49), Pizza by the slice ($1.75), Crazy bread ($1.89)…….
– What item is equivalent?
• 1 Large 14” Pepperoni Pizza at $5.99
• Put these items in order from least expensive to most expensive: (a)
single pepperoni roll, (b) 2 liter beverage, (c) stuffed crazy bread, (d)
pizza by the slice, and (e) crazy bread.
– Single pepperoni roll ($1.50), pizza by the slice ($1.75), crazy bread
($1.89), 2 liter beverage ($1.99), and stuffed crazy bread ($3.99)
Comparing Numbers
• When we compare we use terms such as:
– Less than <
– Greater than >
– Equal to =
• Comparing decimals is similar to comparing whole
numbers.
– 45 < 47
– 150 > 105
• When we compare decimals we use place value or a
number line.
Example 1
Compare Sara’s time with Danny’s time.
Race Results
Name
Time (in seconds)
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1
Step 1: Line up the decimal points
Sara
42.1
Danny 42.5
Step 2: Start at the left and compare
digits. Find the first place where the digits
differ.
42.1
Sara
Danny 4 2 . 5
Step 3: Compare digits that are different
5>1
Therefore, 42.5 > 42.1 and Sara’s
time is less than Danny’s time.
Using a Number Line
Race Results
Name
Time (in seconds)
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1
42.0 42.1
42.5
Numbers to the right are
greater than numbers to
the left.
Since 42.5 is to the right of
42.1 we know 42.5>42.1
Equivalent Decimals
• Decimals that name the same number are
called equivalent decimals.
• We use the “=“ sign for equivalent decimals.
Are 0.6 and 0.60 equivalent?
Are these equivalent?
0.60
=
0.6
Annexing Zeros
• This means placing a zero to the right of the
last digit in a decimal.
• 0.6
0.60
• Although we added a zero, the value of the
decimal did not change!
• Annexing or adding zeros is useful when
ordering a group of decimals.
Ordering Decimals
• Place 15, 14.95, 15.8, and 15.01 in order from
least to greatest
• Step 1: Line up the decimal points
15.00
14.95
15.80
15.01
• Step 2: Annex zeros so that each number has the
same number of decimal places
Ordering Decimals
15, 14.95, 15.8, 15.01
• Step 3: Start at the left and compare digits. Find
the first place where the digits differ.
1 5. 0 0
1 4. 9 5
1 5. 8 0
1 5. 0 1
14.95, 15.00, 15.01, 15.80
• 4 < 5 so 14.95 is the least
• 8 > 0 so 15.80 is the greatest
• 1 > 0 so 15.01 is greater than 15.00
Example 2
• The star Wolf 359 has an apparent magnitude
of 13.5. Suppose another star has an apparent
magnitude of 13.05. Which star has the
smaller magnitude?
13.50
13.05
1 3. 5 0
1 3. 0 0
Step 1: Line up decimals
Step 2: Annex Zeros
Step 3: Start at left and compare digits
5 > 0, so 13.50 > 13.05 and the other star has the
smaller magnitude
Marker board Examples
1. Compare, write <, >, or =.
a. 0.907 ___ 0.6801
b. 14.032 ___ 14.29
a. 0.907 > 0.6801
b. 14.032 < 14.29
2. Order from least to greatest.
a. 0.34, 1.43, 4.034, 1.043, 1.424
a. 0.34, 1.043, 1.424, 1.43, 4.034
b. 1.01, 1.1001, 1.101, 1.0001
b. 1.0001, 1.01, 1.1001, 1.101
Internet Activities
• The Award Ceremony
– http://www.mathsonline.co.uk/nonmembers/gamesroom/
awards/awardc.html
• Decimals in Space
– http://themathgames.com/our-games/decimalgames/place-value/decimal-place-value-math-game
• Builder Ted
– http://www.bbc.co.uk/education/mathsfile/shockwave/ga
mes/laddergame.html
• Ordering Game
– http://www.mathsisfun.com/numbers/orderinggame.php?m=Dec-Tricky
Summarize
1. What are the steps for comparing decimals?
– Step 1: Line up decimals
– Step 2: Annex zeros, if needed
– Step 3: Start at the left and compare digits
2. Why is it important to line up the decimals?
It is important because it keeps the list organized and allows
you to compare digit by digit.
3. Does annexing a zero change the value of the decimal? Why
or why not?
No, because zero is just a place holder when added to the
end of the number.