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.

Compare Sara’s time with Danny’s time. Example 1 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 Race Results Name Time (in seconds) Sara 42.1 Danny 42.5 Ross 42.0 Bethany 40.7 Jacob 46.1 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 Race Results 42.0 42.1 42.5 Name Time (in seconds) Sara 42.1 Danny 42.5 Ross 42.0 Bethany 40.7 Jacob 46.1 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 14.95 15.8 15.01 Step 2: Annex zeros so that each number has the same number of decimal places .00

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. 4. 9 8 5 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 3. 5 13.5 13.05 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 Decimals in Space Builder Ted 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.