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Understanding Decimal Numbers

Understanding Decimal Numbers. Reading Decimals. Say what you see before the decimal Say “and” for the decimal Say what you see after the decimal Say the place value of the final digit To write in words, you write what you say. five hundred eighty and. 5 8 0 . 3 2 4

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Understanding Decimal Numbers

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  1. Understanding Decimal Numbers

  2. Reading Decimals • Say what you see before the decimal • Say “and” for the decimal • Say what you see after the decimal • Say the place value of the final digit • To write in words, you write what you say

  3. five hundred eightyand 5 8 0.3 2 4 three hundred twenty-four thousandths

  4. Hundred thousandths Ten thousands ten thousandths hundreds 20 759 . 16384 tens tenths thousandths ones thousands hundredths

  5. 1 . 46 One and forty-six hundredths

  6. 67 . 4018 sixty seven and four thousand eighteen ten thousandths

  7. 12 304 . 002 Twelve thousand three hundred four and two thousandths

  8. three and forty seven tenths Three and forty seven thousandths 3 . 47 three and forty seven hundredths Three and forty seven hundred

  9. seventeen and eighty-two tenths seventeen and eighty-two hundredths 17 . 082 seventeen thousand eighty two seventeen and eighty-two thousandths

  10. Zero and three thousand two three thousand two ten thousandths 0 . 3002 three thousand two three thousand two thousandths

  11. Sixty four hundredths twenty one Six hundred forty thousand twenty one millionths 0. 640021 Six hundred forty thousand twenty one thousandths Sixty-four thousand twenty one

  12. Modelling Decimal Numbers

  13. Base Ten Blocks

  14. 1 . 4 One and four tenths

  15. One and four tenths

  16. Represents one whole bar Represents one tenth of a bar (meaning you need ten to make a bar) Represents one hundredth of a bar (meaning you need one hundred to make a bar) Represents one thousandth of a bar (meaning you need one thousand to make a bar)

  17. 1.07 One and seven hundredths

  18. One and seven hundredths

  19. 0.53 Fifty-three hundredths

  20. Fifty-three hundredths or 0.53

  21. 1.245 One and two hundred forty-five thousandths

  22. One and two hundred forty-five thousandths or 1.245

  23. 0.006 Six thousandths

  24. Six thousandths or 0.006

  25. 1.013 One and thirteen thousandths

  26. One and thirteen thousandths or 1.013

  27. Two and one hundred seventy-three thousandths or 2.173

  28. four hundred twenty-five thousandths or 0.425

  29. One and two hundred eighty-three thousandths or 1.283

  30. Comparing Decimal Numbers

  31. Which is the larger value?0.129 or 0.31 Prove your choice!

  32. 0.129 0.129 is less than 0.31, so 0.31 is the largest value 0.31

  33. Which is the larger value?0.2 or 0.05 Prove your choice!

  34. 0.2 0.2 is greater than 0.05 0.05

  35. Understanding Decimal Values 45.0076 45.076 673.09 673.1 1098.44 1098.4

  36. 1. Understanding Decimal Values 67.76 67.7600 0.515 0.551 15.099 15.98

  37. Making Connections

  38. nine out of ten nine tenths 0.9 9 10

  39. four tenths four out of ten 0.4 4 10

  40. 7 • 10 two wholes and seven out of ten 2.7 two and seven tenths

  41. Thirty-two out of one hundred 0.32 thirty-two hundredths 32 100

  42. eighty out of one hundred 0.80 eighty hundredths 80 100

  43. six out of one hundred 0.06 six hundredths 6 100

  44. Three and two hundredths 3.02 • 2 • 100 Three wholes and two parts out of a hundred

  45. 2 14 100 Two and fourteen hundredths 2.14 Two wholes and fourteen out of one hundred

  46. Decimals in Expanded Form

  47. Decimals in Expanded Form • Writing decimals in expanded form is an extension of whole numbers in expanded form. • To do this you represent each individual place value EXAMPLE 4.305 is • 4 + 0.3 + 0.005 • 4 x 1 + 3 x 0.1 + 5 x 0.001 • 4 x 100 + 3 x 10-1 + 5 x 10-3

  48. Decimals in Expanded Form • 34.308 • 30 + 4 + 0.3 + 0.008 • 3 x 10 + 4 x 1 + 3 x 0.1 + 8 x 0.001 • 3 x 101 + 4 x 100 + 3 x 10-1 + 8 x 10 -3 • 5.28 • 5 + 0.2 + 0.08 • 5 x 1 + 2 x 0.1 + 8 x .01 • 5 x 100 + 2 x 10-1 + 8 x 10-2

  49. Decimals in Expanded Form 3.49 90.35 • 3 + 0.4 + 0.09 = • 9 x 101 + 3 x 10-1 + 5 x 10-2 = • 40 + 0.8 + 0.003 = • 0.7 + 0.03 + 0.0002 = • 0.06 + 0.4 + 3 + 20 + 0.001 = • 800 + 3 + 60 000 + 0.02 + 0.007 = 40.803 0.7302 23.461 60 803.o27

  50. Decimals in Expanded Form 4000.53 • 4 x 1000 + 5 x 0.1 + 3 x 0.01 = • 7 x 100 + 2 x 0.1 + 5 x 1 + 8 x 0.001 = • 4 x 0.0001 + 3 x 0.1 + 2 x 0.01 = • 0.006 + 0.01 + 700 + 20 + 0.0004 = • 3 x 1 + 4 x 0.01 = • 8 x 100 + 5 x 10-2 + 3 x 10-3 = 705.208 0.3204 720.0164 3.04 8.053

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