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Decimals

Welcome to: UNIT 1c. Decimals. Mr. Zweig’s Math Classes. Clicking on this symbol at the bottom, right hand corner of each page will take you back to this contents page. Back to the WEB. THE BIG QUESTION. So, how do we compare decimals? (anyone know?). Comparing Decimals

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Decimals

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  1. Welcome to: UNIT 1c Decimals Mr. Zweig’s Math Classes Clicking on this symbol at the bottom, right hand corner of each page will take you back to this contents page. • Back to the WEB

  2. THE BIG QUESTION • So, how do we compare decimals? (anyone know?)

  3. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value.

  4. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. So, How do we do this?

  5. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Lets try 0.54 & 0.6 (which is bigger) 0.54 Notice how we line up the decimals 1) Do Rule 1: 0.6

  6. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Lets try 0.54 & 0.6 (which is bigger) 0.54 XX Great… the tenth place doesn’t match! 1) Do Rule 2: One’s place does match 0.6

  7. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Lets try 0.54 & 0.6 (which is bigger) 0.54 The 6 is larger so 0.6 is larger 1) Do Rule 3: 0.6

  8. We have a symbol for “greater than” It looks like this > We say 6 is greater than 5… we can write it this way now… 6 > 5

  9. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. In our last problem we found that 0.6 was greater than 0.54..How do we write it using our new symbol? 0.6 > 0.54

  10. You Did It!!!

  11. Are you ready for another example?

  12. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Try 0.28 & 0.219... (which is bigger)

  13. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Try 0.28 & 0.219...(which is bigger) 0.28 Notice how we line up the decimals 1) Do Rule 1: 0.219

  14. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Try 0.28 & 0.219...(which is bigger) 0.28 XX XX Tenths also matches 1) Do Rule 2: One’s place does match 0.219 We must use hundredths place

  15. Comparing Decimals • Rewrite in a column aligning the decimals. • Compare place values until the numbers do not match in the same place value. • The larger number in a non-matching place value is the larger value. Try 0.28 & 0.219...(which is bigger) 0.28 XX XX Yes! Now do Step 3! 0.28>0.219 0.219

  16. Finally! • Before we end we need to add two more symbols to our bag of tricks

  17. Greater Than >

  18. Less Than <

  19. Equal to =

  20. All three together! • Greater Than Less Than Equal to < > =

  21. < 1. 0.34 ___ 0.35 1. 0.34 ___ 0.35 < 2. 2.3 ___ 2.34 2. 2.30___ 2.34 > • 4.5 ___0.45 • 4.5 ___0.45 < 4. 0.5692 ___ 0.596 4. 0.5692 ___ 0.596 = 5. 0.8 ___0.80 5. 0.80___0.80

  22. 4.1, 0.41, 1.41, 0.14, 0.144 0.410 1.410 0.140 0.144 0.41 1.41 0.14 0.144 0.140, 0.144, 0.410, 1.410, 4.100

  23. 0.98, 9.8, 9.88, 9.89, 9.98 9.8 9.88 9.89 9.98 9.80 9.88 9.89 9.98 0.98, 9.80, 9.88, 9.89, 9.98

  24. 1) 3.3, 3.33, 3.03, 0.3, 0.33 0.3, 0.33, 3.03, 3.3, 3.33 • 0.007, 0.7, 0.077, 0.77 0.007, 0.077, 0.7, 0.77 3) 5.6, 0.56, 0.056, 0.556, 0.5655 0.056, 0.556, 0.56, 0.5655, 5.6

  25. Rounding Decimals Find the place value we are rounding to (named or underlined). Look one place to the right. If this place value (the one to the right) is 5 or more, it is half way or more and the named place value goes up by one digit. If not one to the right is not 5 or more, it is not half way. The underlined digit stays the same. Make everything to the right of the named place value zero. 3,458.45 One to the right is 8 (5 or more) 3,460 3,458.45 One to the right is 4 (less than 5) 3,000

  26. 4,537.89 4,540 7 is larger - UP 4,561.89 4,560 1 is smaller - STAY 4,967.89 5,000 6 is larger - add one 4,567.89 5,000 5 tie - add one 4,567.89 4,568 8 is larger - add one 4,567.39 4,567 3 is smaller - STAY

  27. 0.4928 4 is less than 5 0 8 is greater than 5 0.6 0.582 0.6 9 is greater than 5 0.5992 3 is less than 5 0.12 0.1234 0.827 7 is greater than 5 0.83

  28. Yeah! THE END!

  29. OPEN YOUR TEXTBOOKS NOW • Take out a piece of paper • Go to Page 54 & 55 • Do the following problems 1,2,3,4,5,6,7,8,9,10,11,12,13, 15, 20,23,26, 27, 35.37.42.43, 44, 46, 54,

  30. Prompt Some of the digits in the following numbers are hidden. A. 3 . ▒ ▒ ▒ B. 3 . ▒ ▒ Give an example when each situation is true. Using mathematics, justify your answers. 1. the value of A is larger than the value of B 2. the value of B is larger than the value of A 3. the value of A is equal to the value of B

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