Decimals and

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Decimals and Place Value
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The zero and the counting numbers (1,2,3,...)
make up the set of whole numbers. But not every
number is a whole number. Our decimal system lets
us write numbers of all types and sizes, using a
clever symbol called the decimal point. As you
move right from the decimal point, each place
value is divided by 10.    

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In our number system, digits can be placed to the
left and right of a decimal point, to indicate
numbers greater than one or less than one. The
decimal point helps us to keep track of where the
"ones" place is. It's placed just to the right of
the ones place. As we move right from the decimal
point, each number place is divided by 10.
Tenths
Tens
Ones
Thousandths
Hundredths
Hundreds
and
5
2
1
4
3
6
4
Watch the 9's for place value.
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Beyond the set of whole numbers, there are
numbers that are less than one, but, greater than
zero they are known as fractional parts. The
name lends itself well, as these numbers are
parts, or fractions, of one whole.
The rectangle, or whole, above has been divided
into 10 equal parts, or tenths.
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The rectangle is 1 whole.
If I place the rectangle with 10 equal parts over
the whole I can see how 10 tenths 1 whole.
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The hundredths place has 100 equal parts.
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The rectangle is 1 whole.
If I place the rectangle with 100 equal parts
over the whole I can see how 100 hundredths 1
whole.
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What would six tenths look like?
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How many tenths are shaded in?
0.4
11
0.8

____________
0.4

____________
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What would thirty hundredths look like?
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How many hundredths are shaded in?
0.20
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0.30

____________
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0.58

____________
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Decimals are equivalent, or to decimals in
other place values.
one tenth ten hundredths
Use your decimal squares to find
one tenth _____ thousandths
100
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three tenths ______ hundredths
thirty
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seven tenths ______ hundredths
seventy
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Whole Number Portion The whole number portion of
a decimal number are the digits to the left of
the decimal place. Example In the number
23.65, the whole number portion is 23. In the
number 0.024, the whole number portion is 0
There is nothing there!
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Which number is the whole number?
51.05
51
3.17
3
0.97
0
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The whole number is to the left of the decimal.
70.006
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Less Than A Whole Number Portion The less than a
whole number (or fractional parts) portion of a
decimal number are the digits to the right of the
decimal place. Example In the number 23.65,
the less than a whole number portion is 65. In
the number 0.024, the less than a whole number
portion is 024.
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Which number is the less than the whole number?
34.77
77
2.09
09
0.1
1
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The less than whole number is to the right of
the decimal.
99.321
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Hint 1 Remember to read the decimal point as
"and" -- notice in the two numbers below what a
difference that makes!
0.548
500.048
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Hint 2 When writing a decimal number that is
less than 1, a zero is normally used in the ones
place
0.526 not .526
A symbol for nothing--our zero--had to be
invented. Zero "holds the place" for a particular
value, when no other digit goes in that position.
For example, the number 0.506" in words means no
ones, 5 tenths, no hundredths and 6 thousandths.
Without a symbol for nothing, our decimal number
system wouldn't work.
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Writing Word Names For Decimals

• Look to see if there is a number to the left of
  the decimal if so write it out. If there is no
  number to the left of the decimal, skip to step.
  
• Write an and for the decimal point.
• Write out the number to the right of the decimal.
  Do not yet include the place value.
• Determine the place value of the last digit to
  the right of the decimal. Write the place value.

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Lets Practice
9.53
nine
and
hundredths
fifty three
0.50
fifty hundredths
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On your own paper write the word names for each
decimal.
500.006
2.60
0.8
0.71
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500.006
five hundred and six thousandths
0.71
seventy one hundredths
2.60
two and sixty hundredths
0.8
eight tenths
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How would you write these numbers in decimal
form?
321.7
three hundred twenty one and seven tenths
0.548
five hundred forty eight thousandths
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Writing Decimals in Fraction Form
Let's try to figure out the fractional
equivalent of the decimal .345. The 3
represents 3 tenths,the 4 represents 4
hundredthsthe 5 represents 5 thousandths So,
we can write .345 3/10 4/100 5/1000.
or
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Here's a shortcut for dealing with decimals
Instead of writing out .345 3/10 4/100
5/1000, then finding the common denominator,
adding, and reducing, just think
1. Ask yourself What is the number?
345
2. Ask yourself What is the place value?
thousandths
3. Then place the 345 over the 1000.
345 1000
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Lets Practice
53 100
801 1000
0.53
0.801
3 10
0.3
0.60
60 100
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Ordering Decimals
3.50
3.83
3.45
3.09
Write them in columns so the place values line up.
Compare the digits in each column, starting at
the left.
o
o
Which pizza is cheapest?
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Log Book
How many hundredths are in four tenths? Explain
how you know and draw an example.
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There are forty hundredths in four tenths. I
know this because one tenth is equal to 10
hundredths. So 10 10 10 10 0.40.
If you lay them on top of each other they are
the same.