Introduction to decimals

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
5 8 0 .3 2 4
three hundred twenty-four
thousandths

4. Ten
thousands
tenths
hundredths
ones
hundreds
thousands
tens
thousandth
s
ten
thousandth
s
Hundred
thousandth
s

5. One
and
forty-six hundredths

6. sixty seven
and
four thousand eighteen
ten thousandths

7. Twelve thousand
three hundred four
and
two thousandths

9. Base Ten
Blocks

10. One
and
four tenths

11. One and
four tenths

12. 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)

13. One
and
seven hundredths

14. One and seven
hundredths

15. Fifty-three
hundredths

16. Fifty-three
hundredths or
0.53

17. One and two hundred
forty-five
thousandths

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

19. Six thousandths

20. Six thousandths
or 0.006

21. One and thirteen
thousandths

22. One and thirteen
thousandths or
1.013

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

24. four hundred
twenty-five
thousandths or
0.425

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

27. nine out
of ten
0.9
9
10
nine tenths

28. four out
of ten
0.4
four tenths
4
10

29. 2.7
two and
seven tenths
two wholes
and seven out
of ten
2 7
10

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

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

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

33. Three and
two
hundredths
3 2
100
3.02
Three
wholes and
two parts out
of a hundred

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

36. 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

37. 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

38. Decimals in Expanded Form
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 =
3.49
40.803
23.461
60
803.o27
0.7302
90.35

39. Decimals in Expanded Form
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 =
4000.53
705.208
720.0164
3.04
0.3204
8.053

41. 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
If the digit is:
 4 or lower – leave the same
Digits past the rounded digit are not recorded
in the rounded number.

42. 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.

43. Example
34.561 rounded to the nearest tenth
is . . .
3 4 . 5 6 1
34.6

44. Example
4.6341 rounded to the nearest
hundredth is . . .
4 . 6 3 4 1
4.63

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

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

47. Example
5.96 rounded to the nearest tenth
is . . .
5 . 9 6
6

48. Example
587.469 rounded to the nearest
whole number is . . .
5 8 7 . 4 6 9
587

49. Example
7535.9 rounded to the nearest whole
number is . . .
7 5 3 5 . 9
7536

50. Example
619.844 rounded to the nearest whole
number is . . .
6 1 9 . 8 4 4
620

51. Example
6198 rounded to the nearest hundred
is . . .
6 1 9 8
6200

52. Example
463 228 rounded to the nearest
hundred thousand is . . .
463 228
500
000

54. 8 x 0.3 =
Eight groups with three
tenths in each group
2.4

55. 2 x 1.6 =
Two groups with one and
six tenths in each group
3.2

56. 4 x 0.9 =
Four groups with nine
tenths in each group
3.6

57. 9 x 0.5 =
Nine groups with five
tenths in each group
4.5

58. 2 x 1.2 =
Two groups with one and
two tenths in each group
2.4

60. 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 1 7
10