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 eighty and
three hundred twenty-four thousandths

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

5. 1 . 46
One
and
forty-six hundredths

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

7. Twelve thousand three hundred four and
Twelve thousand three hundred four and
two thousandths

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

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

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

11. 0. 640021 Sixty four hundredths twenty one
Six hundred forty thousand twenty one millionths
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. one thousandth of a bar (meaning you
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. One and two hundred forty-five thousandths
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. One and thirteen thousandths
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
45.076
673.09
673.1
1098.4

36. 1. Understanding Decimal Values
67.76
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. two wholes and seven out of ten7 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
Three and two hundredths
3.02 2
100
Three wholes and two parts out of a hundred

45. Two and fourteen hundredths
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 is
4 x x x 0.001
4 x x x 10-3

48. Decimals in Expanded Form
34.308
3 x x x x 0.001
3 x x x x 10 -3
5.28
5 x x x .01
5 x x x 10-2

49. Decimals in Expanded Form
3.49 =
9 x x x 10-2 = = = = =
90.35
40.803
0.7302
23.461
o27

50. Decimals in Expanded Form
4 x x x 0.01 =
7 x x x x =
4 x x x = =
3 x x 0.01 =
8 x x x 10-3 =
0.3204
3.04
8.053

51. Rounding Decimals

52. Rounding Decimals
When rounding decimals it is first necessary to identify the place value you are rounding to.
The digit that follows will tell you whether you should round up or leave the digit the same.
If the digit is:
5 or higher – round up by one
4 or lower – leave the same
Digits past the rounded digit are not recorded in the rounded number.

53. When rounding it is helpful if you . . .
Circle the place value you are rounding to.
Underline the digit that follows; it is this digit that tells you to round up or leave the same.

54. Example
rounded to the nearest tenth
is . . .
34.6

55. Example 4 . 6 3 4 1 4.6341 rounded to the nearest hundredth is . . .

56. Example 6 7 . 1 1 2 5 67.1125 rounded to the nearest thousandths is
67.113

57. Example 0 . 6 9 7 1 .6971 rounded to the nearest hundredth is . . .
.70

58. Example
5.96 rounded to the nearest tenth
is . . . 6

59. Example
rounded to the nearest whole number is . . .
587

60. Example
rounded to the nearest whole number is . . .
7536

61. Example
rounded to the nearest whole number is . . .
620

62. Example
6198 rounded to the nearest hundred is . . .
6200

63. Example
rounded to the nearest hundred thousand is . . .

64. Multiplying Decimals

65. Eight groups with three tenths in each group
8 x 0.3 =
2.4
Eight groups with three tenths in each group

66. Two groups with one and six tenths in each group
3.2
Two groups with one and six tenths in each group

67. Four groups with nine tenths in each group
4 x 0.9 =
3.6
Four groups with nine tenths in each group

68. Nine groups with five tenths in each group
9 x 0.5 =
4.5
Nine groups with five tenths in each group

69. Two groups with one and two tenths in each group
2 x 1.2 =
2.4
Two groups with one and two tenths in each group

71. Question # 9 Example
To share 1.7 of a bar I would need two bars. I would give away one whole bar and break the second bar into ten equal pieces and give away seven pieces of the ten or one and seven tenths.
One and seven tenth as a fraction is 10