What is a Decimal

1
What is a Decimal?
2
What is a decimal?

• A decimal is similar to a fraction in that it
  is not a whole number. It is a part of a number.
  We use decimals most often when we are talking
  about money.
• 13.45
• How would you read this number?

3
13.45

• Thirteen dollars and forty five cents.
• Remember
• You do not need to use the when your money
  amount is greater than 1.

4
What does the .45 mean?

• .45 is the same thing as saying 45 . It means
  that it is only a part of a dollar. It is not
  the whole dollar. We still need more to get the
  whole thing.

5
Why do I have to understand decimals?

• This is a good question. We need to
  understand what the value of each number means in
  order to understand what we are talking about.
  Here is an example
• A shirt costs 12.05, but when I wrote the
  number down I wrote 12.5. What is wrong with
  this?

6
Why is 12.5 wrong?

• 12.5 really is saying 12.50, because when we
  read how much something costs it always has two
  places after the decimal point. If we dont have
  a number after the first number we must assume it
  is a zero. However, when we read 12.05, the
  zero is the place holder so we know it is 5 and
  not 50. That is a 45 difference. I can get a
  piece of gum for that amount!

7
Lets Look at Some Place Value
8
How do I read a decimal?

• If you look at the number 12.3, you say 12 and 3
  tenths.
• If you look at the number and it says 12.35, you
  say 12 and 35 hundredths.
• If you look at a number and it says 12.05, you
  say 12 and 5 hundredths.
• Now you practice saying them!

9
Lets Write this in Expanded Notation
If we are using money, it would look like this
100 30 7 80 2 137.82
If we are not using money, it would look like
this
100 30 7 .8 .02 137.82
10
How do I know how large a decimal is?

• If you see two numbers that are decimals, one
  says 7.3 and the other says 7.003, you look at
  how many places the number that is longer has.
  You make both numbers the same length by adding
  zeros to the end of the shorter number. So the
  numbers read
• 7.300 or 7.003
• Now when you look at the number you can see which
  is larger 7.300

11
Which is larger?

• 4.5 or 4.05
• Because 4.5 equals 4.50, 50 is larger than 5
• 2) 6.003 or 6.3
• Because 6.3 equals 6.300, 300 is larger than 3
• 3) 5.012 or 5.12
• Because 5.12 equals 5.120, 120 is larger than 12

4.5
6.3
5.12
12
When else do we use decimals?

• Weight (He weighed 85.5 lbs)
• Temperature (It was so cold today, it was only
  43.7)
• Measuring distances (example, the race was a 5 K,
  but since I dont understand kilometers, I
  changed it to miles and saw that the race was 3.1
  Miles long)
• Can you think of any other times?

13
Meet the Base Ten Blocks

• This is a flat. It is made up of ten rows and
  ten columns of small blocks.
• Its value is 1.

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Meet the Base Ten Blocks

• This is a rod. It is made up of ten rows and
  one column of small blocks.
• Ten rods make a flat.
• Its value is one tenth since ten rods make one
  flat.
• We write that 0.1

15
Meet the Base Ten Blocks

• This is a block. It is a small cube.
• There are 10 blocks in a rod. There are 100
  blocks in a flat.
• Its value is one hundredth since one hundred
  blocks would make one flat.
• We write that 0.01

16
Multiple Base Ten Blocks

• Three flats would have the value of 3.

17
Multiple Base Ten Blocks

• Four rods would have the value of four tenths.
• We write that 0.4
• Note that its value is also 40 hundredths since
  there are 40 blocks here.
• So it could also be written 0.40

18
Multiple Base Ten Blocks

• Six blocks would have the value of six
  hundredths.
• We write that 0.06

19
Multiple Base Ten Blocks

• One flat and two rods would have the value one
  and two tenths.
• We write that 1.2

20
Multiple Base Ten Blocks

• One rod and two blocks would have the value one
  tenth and two hundredths.
• Its value is the same as twelve hundredths.
• We write that 0.12

21
Multiple Base Ten Blocks

• One flat, three rods and four blocks would have
  the value one, three tenths and four hundredths.
• Its value is the same as one and thirty four
  hundredths.
• We write that 1.34

22
Multiple Base Ten Blocks

• One flat, one rod and 6 blocks would have the
  value one, one tenth, and six hundredths.
• That also equals one and 16 hundredths.
• How would we write that?

1.16
23
Multiple Base Ten Blocks

• One flat and two blocks would have the value one
  and two hundredths.
• How would we write that?

1.02
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Decimal Practice

• Whats the value?

One and five hundredths
How do we write that?
1.05
25
Decimal Practice

• Whats the value?

Two and thirteen hundredths
How do we write that?
2.13
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Decimal Practice

• Whats the value?

One and fifty one hundredths
How do we write that?
1.51
27
Show with blocks
One and twenty three hundredths
How do we write that?
1.23
28
Show with blocks
One and six tenths
How do we write that?
1.6
29
Show with blocks
One and eight hundredths
How do we write that?
1.08
30
Show with blocks
2.3
How do we say that?
Two and three tenths
31
Show with blocks
0.46
How do we say that?
Forty six hundredths
32
Trading Blocks

• Ten blocks can be traded for a rod.

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Trading Blocks

• A flat can be traded for ten rods.

34
Addition

• Add
• 1.3 0.2

The sum is 1.5
35
Addition

• Add
• 1.2
• 1.04

The sum is 2.24
36
Addition

• Add
• 0.34 1.01

The sum is 1.35
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Addition

• Add
• 0.04 0.08

The sum is 0.12
38
Addition

• Add
• 1.29 0.2

The sum is 1.49
39
Addition

• Add
• 1.29 0.02

The sum is 1.31