Reading Decimals

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
Six hundred forty thousand twenty one millionths
Sixty four hundredths twenty one
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
Represents one thousandth of a bar
Represents one hundredth of 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 is less than 0.31, so 0.31 is the largest
value
33
Which is the larger value?0.2 or 0.05

• Prove your choice!

34
0.2 is greater than 0.05
35
Understanding Decimal Values
45.0076
45.076
673.09
673.1
1098.4
1098.44
36
1. Understanding Decimal Values
67.76
67.7600
0.515
0.551
15.98
15.099
37
nine out of ten
nine tenths
0.9
9 10

38
four tenths
four out of ten
0.4
4 10

39

• 7
• 10

two wholes and seven out of ten

2.7
two and seven tenths


40
Thirty-two out of one hundred










0.32
thirty-two hundredths
0.32
41










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










0.06
six hundredths
6 100
43
Three and two hundredths
3.02

• 2
• 100

Three wholes and two parts out of a hundred
 
44
2 14 100
Two and fourteen hundredths
2.14
Two wholes and fourteen out of one hundred
 
45
Decimals in Expanded Form
46
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

47
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
• 5.28
• 5 0.2 0.08
• 5 x 1 2 x 0.1 8 x .01

48
Decimals in Expanded Form
3.49

• 3 0.4 0.09
• 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
49
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

705.208
0.3204
720.0164
3.04
50
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

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
• If the digit is
• 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

• 34.561 rounded to the nearest tenth
• is . . .
• 3 4 . 5 6 1

34.6
55
Example

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

4.63
56
Example

• 67.1125 rounded to the nearest thousandths is
• 6 7 . 1 1 2 5

67.113
57
Example

• .6971 rounded to the nearest hundredth is . . .
• 0 . 6 9 7 1

.70
58
Example

• 5.96 rounded to the nearest tenth
• is . . .
• 5 . 9 6

6
59
Example

• 587.469 rounded to the nearest whole number is .
  . .
• 5 8 7 . 4 6 9

587
60
Example

• 7535.9 rounded to the nearest whole number is . .
  .
• 7 5 3 5 . 9

7536
61
Example

• 619.844 rounded to the nearest whole number is .
  . .
• 6 1 9 . 8 4 4

620
62
Example

• 6198 rounded to the nearest hundred is . . .
• 6 1 9 8

6200
63
Example

• 463 228 rounded to the nearest hundred thousand
  is . . .
• 463 228

500 000
64
Multiplying Decimals
65
8 x 0.3
2.4
Eight groups with three tenths in each group








66
2 x 1.6
3.2
Two groups with one and six tenths in each group




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




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









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




70
(No Transcript)
71
Estimating Decimals