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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
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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 Race Results Compare Sara’s time with Danny’s time. 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. Sara Danny 4 2 . 1 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 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 Race Results 42.0 42.1 42.5
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 14.95 15.8 15.01 • Step 2: Annex zeros so that each number has the same number of decimal places .00 0
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 1 1 1 5. 4. 5. 5. 0 9 8 0 0 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? 1 1 3. 3. 5 0 0 0 13.5 13.05 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 • Compare, write <, >, or =. • 0.907 ___ 0.6801 • 14.032 ___ 14.29 • Order from least to greatest. • 0.34, 1.43, 4.034, 1.043, 1.424 • 1.01, 1.1001, 1.101, 1.0001 a. 0.907 > 0.6801 b. 14.032 < 14.29 a. 0.34, 1.043, 1.424, 1.43, 4.034 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/decimal-games/place-value/decimal-place-value-math-game • Builder Ted • http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html • Ordering Game • http://www.mathsisfun.com/numbers/ordering-game.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 • 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. • 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.