Concepts
1 BasicFunctions
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Unit 1C
Review of Operations with
Decimal Fractions and Percent
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1.10
Addition and Subtraction of
Decimal Fractions
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Introduction to Decimals
4
Introduction to Decimals
A fraction whose denominator is 10, 100, 1000, or any
power of 10 is called a decimal fraction.
Decimal calculations and measuring instruments calibrated
in decimals are the basic tools for measurement in the
metric system.
The common use of the calculator makes a basic
understanding of decimal principles necessary.
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Introduction to Decimals
We know that the place values of the digits of a whole
number.
Each digit to the left of the decimal point represents a
multiple of a power of 10.
Each digit to the right of the decimal point represents a
multiple of a power of
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Introduction to Decimals
Study Table 1.2, which shows place values for decimals.
Note that 100 = 1.
Table 1.2
Place Values for Decimals
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Example 1
In the number 123.456, find the place value of each digit
and the number it represents.
We know that place values to the left of the decimal point
are powers of 10 and place values to the right of the
decimal point are powers of
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Introduction to Decimals
Often, common fractions are easier to use if they are
expressed as decimal equivalents.
Every common fraction can be expressed as a decimal.
A repeating decimal is one in which a digit or a group of
digits repeats again and again; it may be written as a
common fraction.
A bar over a digit or group of digits means that this digit or
group of digits is repeated without ending.
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Introduction to Decimals
Each of the following numbers is a repeating decimal:
0.33333 . . . is written
72.64444 . . . is written
0.21212121 . . . is written
6.33120120120 . . . is written
A terminating decimal is a decimal number with a given
number of digits.
Examples are 0.75, 12.505, and 0.000612.
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Introduction to Decimals
Changing a Common Fraction to a Decimal
To change a common fraction to a decimal, divide the
numerator of the fraction by the denominator.
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Example 4
Change
to a decimal.
Divide the numerator by the denominator.
(a terminating decimal)
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Introduction to Decimals
Since a decimal fraction can be written as a common
fraction with a denominator that is a power of 10, it is easy
to change a decimal fraction to a common fraction.
Simply use the digits that appear to the right of the decimal
point (disregarding beginning zeros) as the numerator.
Use the place value of the last digit as the denominator.
Any digits to the left of the decimal point will be the
whole-number part of the resulting mixed number.
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Introduction to Decimals
In on-the-job situations, it is often more convenient to add,
subtract, multiply, and divide measurements that are in
decimal form rather than in fractional form.
Except for the placement of the decimal point, the four
arithmetic operations are the same for decimal fractions as
they are for whole numbers.
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Introduction to Decimals
Adding or Subtracting Decimal Fractions
Step 1: Write the decimals so that the digits having the
same place value are in vertical columns. (Make
certain that the decimal points are also lined up
vertically.)
Step 2: Add or subtract as with whole numbers.
Step 3: Place the decimal point between the ones digit and
the tenths digit of the sum or the difference. (Be
certain the decimal point is in the same vertical line
as the other decimal points.)
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Example 10
Perform the indicated operations: 51.6 – 2.45 + 7.3 – 14.92
difference
sum
final difference
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