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Understanding Place Value and Decimal Operations

Learn how to identify the place value of numbers, compare and order decimals, round decimals, and perform operations with decimals.

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Understanding Place Value and Decimal Operations

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  1. Ms. Crusenberry 9-2013

  2. Place Value

  3. Name the Place Value of the Underlined Number • 867.43 • 6.2395 • 148.372 • 9.3765

  4. Answers • Hundredths • Tenths • Thousandths • Ten-thousandths

  5. Comparing Ex: 19.368 __<___19.37 19.368 19.370 All numbers are the same until you get to 6 in the first set and 7 in the second set. The 7 is bigger; therefore 19.370 is the larger number.

  6. Practice • 3.6 _____ 3.486 • 17.228 _____ 17.28 • 0.023 _____ 0.00981 • 3.537 _____ 3.536

  7. Answers • > • < • > • >

  8. Multiple Numbers Which numeral is the largest? • 5.332 5.359 5.317 • 14.04 14.198 14.2 • 9.308 9.3 9.299

  9. Answers • 5.332 5.359 5.317 • 14.04 14.198 14.2 • 9.308 9.3 9.299

  10. Ordering Decimals You do this based on their place value. Ex: smallest to largest 3.06 3.219 3.058 answer: 3.058 3.06 3.219Ex: largest to smallest 6.534 6.5 6.098 answer: 6.534 6.5 6.098

  11. Practice – Smallest to Largest • 12 11.98 12.006 • 6.08 6.8 6.76 • 4.368 4.3 4.319 • 72.008 72.01 72.0

  12. Answers • 11.98 12 12.006 • 6.08 6.76 6.8 • 4.3 4.319 4.368 • 72.0 72.008 72.01

  13. Practice – Largest to Smallest • 8 7.09 8.2 • .903 .95 .921 • 7.9 7.902 7.829 • 11.361 11.35 11.3

  14. Answers • 8.2 8 7.09 • .95 .921 .903 • 7.902 7.9 7.829 • 11.361 11.35 11.3

  15. Rounding Decimals • Rule – the number 5 or above to the right of the place value you are rounding to makes the number go up by one; 4 or less the number stays the same Ex. Round to the nearest tenth 4.569 = 4.600

  16. Practice Round to the nearest tenthsa) 2.34 b) 42.25 c) 14.6458Round to the nearest hundredthsd) 5.823 e) 2.124 f) .066 Round to the nearest thousandths g) 2.12394 h) 6.75689 i) .00057

  17. Answers • 2.30 • 42.30 • 14.6500 • 5.820 • 2.120 • .070 • 2.12390 • 6.75690 • .00060

  18. Adding Decimals • Rule – you must line up the decimals; fill in with zeros if neededEx: 2.3 + 5 + .68 2.30 5.00+0.68 7.98

  19. Practice • 4.57 + 3.9 + 26 + 3.298 • 17 + .352 + 6.7 + 42.06 • .663 + 48 + .43 + 37 • 5.058 + .7 + 9.006 + .49

  20. Answers • 37.768 • 66.112 • 86.093 • 15.254

  21. Subtracting Decimals • Rule – the same rule applies here that you did in adding decimals: line up the decimals and add zeroes if need beEx: 12.5 – 4.2 12.5 - 4.2 8.3

  22. Practice • 15.6 – 2.34 • 5.8 – 2.14 • 5.2 - .423 • 14.6 - 12

  23. Answers • 13.26 • 3.66 • 4.777 • 2.6

  24. Multiplying Decimals • Rule – when multiplying decimals, count the number of decimal places in the problem to determine where to put the decimal point in the answerEx: 2.31 x 4.2 2.31 two placesx 4.2 one place 4629240 9.702 three places

  25. Practice • 2.3 x 4.5 • 8.71 x 2.6 • 355 x 2.78 • 23.45 x 1.8

  26. Answers • 10.35 • 22.646 • 986.9 • 42.21

  27. Dividing Decimals Diving by a whole number • Rule – do not move the decimal inside the division house, bring it up into the answer. 5.3 Ex: 7 37.1-35 21-21 0

  28. Continued Dividing by a decimal • Rule – move the decimal outside the division house the amount of places you need to make a whole numberRule 2 – however many places you move the decimal outside of the division house, you must move it that many places on the inside of the division house

  29. Example No. 1 12.6 .6 7.56 so 6 75.6-6 15-12 36 -36 0

  30. Example No 2 **you will have to add a decimal and a 0 in order to move it inside the division house 4. .5 2 .5 2.0 5 20. -20 0

  31. Practice • 21.04 ÷ 8 • 37.38 ÷ 6 • 9.36 ÷ .6 • 13.95 ÷ .9 • 47 ÷ .8 • 315 ÷ .9

  32. Answers • 2.63 • 6.23 • 15.6 • 15.5 • 58.75 • 350

  33. Renaming Fractions as Decimals • Rule – Remember your decimal place value

  34. Examples Rule - Place value is determined by the last number of the decimal; then reduce as needed .012 = 12/1000 = 3/250 .65 = 65/100 = 13/20 .7 = 7/10

  35. Practice • .82 • .0198 • .40 • 3.84 • .19 • .248

  36. Answers • .82 = 82/100 = 41/50 • 198/10,000 = 99/5000 • 40/100 = 4/10 = 2/5 • 3 84/100 = 3 21/25 • 19/100 • 248/1000 = 31/125

  37. Renaming Fractions as Decimals • Rule – Divide the numerator by the denominator .3 Ex. 3/10 10 3.0 -3 0 0

  38. Practice • 2/5 • 9/100 • 16/25 • 3/40 • 9/16 • 7/10

  39. Answers • .4 • .09 • .64 • .075 • .5625 • .7

  40. Repeating Decimals Ex. 3/11 .2727 **use rounding rules answer is .273 11 3.0000- 2 2 80-77 30-22 80-77

  41. Practice **divide to four places, round to three places • 19/22 • 2/33 • 5/6 • 4/9 • 10/11 • 2/3

  42. Answers • .864 • .061 • .833 • .445 • .909 • .667

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