Decimal Basics

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Decimal Basics
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Our number system is sometimes referred to as a
Decimal System. We also use the word decimals to
describe numbers represented with a decimal
point. In some countries a comma is used for the
decimal point.
5.2
666.33
0.007
Decimals and the metric system of measurement
became widely used in Europe during the French
Revolution.
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5.2
It is common to call 5.2, five point two . In
this class, please use the more descriptive
five and two tenths.
It is common to call 0.007, point zero zero
seven. In this class, please use the more
descriptive seven thousandths.
0.007
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Connect decimal numbers with fractions.
Decimal numbers are used to represent fractions
that have a denominator of 10, 100, 1000 or some
other power of ten.
0.001 1/1000
0.3 3/10
0.37 37/100
Note that the number of digits after the decimal
point is the same as the number of zeros in the
denominator of the equivalent fraction.
Mixed numbers have a whole and a fraction part.
Decimal numbers greater than one have a whole
and a decimal part.
4.7 4 7/10
82.09 82 9/100
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Decimal numbers have the same names as their
fractional representations.
0.3 3/10
three tenths
0.37 37/100
thirty seven hundredths
0.001 1/1000
one thousandth
eighty two and nine hundredths
82.09 82 9/100
4.7 4 7/10
four and seven tenths
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Connect decimal numbers to Base-10.
Our whole numbers are based on ten .
slow
1
10
times ten is
times ten is
100
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Decimal numbers are based on ten just like our
whole numbers.
Suppose now that this is 1.
slow
Divide one by ten to get one tenth
0.1
1
slow
Now divide one tenth by ten to get one hundredth.
0.01
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It is common to use a square to represent 1. The
large square below represents 1. (the whole)
Each row represents 0.1. (one tenth)
Each small square represents 0.01. (one
hundredth)
1
0.1
0.01
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Standard Algorithms for Performing Operations on
Decimal Numbers
We are able to use the same algorithms for
numbers with decimal points as we do with whole
numbers. We just need to make adjustments to
insure that our decimal point ends up in the
correct spot. To see why we put the decimal
point where we do, we will compare the decimal
algorithms with those for fractions.
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Addition Algorithm
Note the relationship between finding the Least
Common Denominator, 1000, and lining up the
decimal points.
Decimal problem
Equivalent fraction problem
3.026 26.7 8.52
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Multiplication Algorithm
Note the relationship between the digits to the
right of the decimal point in the decimal
product, and the number of zeros in the
denominator of the fractional product.
Decimal problem
Equivalent fraction problem
.21 x .7 .147
In the decimal algorithm, we count the digits to
the right of the decimal point in the factors,
and place the decimal point in the product so
that the same number of digits are to the right
of it. In the fraction algorithm, we multiply
the powers of ten in the denominators of the
factors. This results in a power to ten with the
same number of zeros as the two factors.
Try out the decimal and fraction algorithms for
5.017 x 0.3.
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Division Algorithm
In the decimal algorithm, we move the decimal
point of the divisor to the right until we have a
whole number. We then move the decimal point of
the dividend the same number of places. Then we
use the whole number division algorithm. Remember
that division can be represented as a fraction as
above in a fractional version of the problem. By
multiplying the numerator and denominator by the
same power of ten, we obtain a whole number in
the denominator. We are actually doing the
same thing when we move the decimal point in the
decimal long division algorithm. Because we
multiply both the divisor and dividend (or
numerator and denominator) by the same number, we
do not alter the quotient.
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Keep in mind that it is fine if you remember how
to do the operations with decimals. However, if
this were all there was that you needed to know
about decimals, students would just be given a
calculator and that would be that.
This course is about the whys. To understand
more about decimals, you need to explore and play
with them.
Right click and select End Show. Then Close to
return.