Transcript POSITIVE EXPONENTS

Powers of Ten
Positive Exponents
 Negative Exponents
 Multiplication In Powers Of Ten Form
 Division In Powers Of Ten Form
 Combined Multiplication And Division In
Powers Of Ten
 Scientific Notation
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Powers of Ten (cont.)
Problems With Complex Denominators Or
Numerators
 Reciprocals
 Powers And Roots In Base Ten
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Positive Exponents
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Large or small numbers can be handled easily by
using a system of notation called powers of ten.
The powers of ten refers to the exponents of ten. This
exponent is the number of times ten is multiplied by
itself. For example 10 x 10 x 10 x 10 = 104. The four
is the exponent of ten.
Exponents determine the number of places the
decimal point is moved from the present decimal
point toward the new decimal point.
If no number is given with the power of ten, insert 1.
An example is 103 = 1. x 103 = 1000.
4.56 x 103 = 4560. Notice the decimal point moved to
right with a positive exponent.
To convert from a powers of ten to a number, simply
write 1 and follow it by the number of 0's in the
exponent if the exponent is a positive number.
Negative Exponents
Numbers less than 0 are dealt with by
using negative exponents.
 Negative exponents determine the number
of places the decimal point is moved from
the present decimal point towards the left
to the new decimal point.
 An example of this is 10-3 = 0.001.
 Also 78.9 x 10-4 =.00789
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Multiplication In Powers Of Ten Form
Multiplication of terms with powers of
10 is simply a matter of adding the
powers.
 105 x 103 = 108
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Division In Powers Of Ten Form
Division of numbers containing powers of
ten involves subtraction of the exponents.
 103/102 = 101
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Combined Multiplication And
Division In Powers Of Ten
This process is one of adding or subtracting
the powers of ten as required.
 The powers of ten are added or subtracted
using the same rules as adding or
subtracting signed numbers.
 To move a power of ten from a
denominator to a numerator, simply change
the sign of the exponent. 1/103 = 10-3. The
opposite change is also true.
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Scientific Notation
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A very convenient method of expressing the
numbers we use in electronics is the use of
scientific notation.
Scientific notion is the placing of a decimal point
after the MSD and adding a power of ten.
The exponent of the power of ten will be the
number of places the decimal point is moved.
In the original number, count the number of
decimal places the decimal point moves left. This
is the positive value of the exponent.
Move the decimal point to the right and the
exponent is negative.
Problems With Complex
Denominators Or Numerators
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If your problem has a complex denominator or
numerator, the fraction line says that everything in the
numerator is surrounded by imaginary parentheses and
must be done first.
Likewise everything in the denominator has a pair of
parentheses and must be combined before the division
takes place. This is also the clue on how to do this with
your calculator.
Reciprocals
A reciprocal of a number is one divided by
that number.
 A reciprocal of a fraction (like 2/3) is that
fraction flipped over (3/2).
 Most calculators have a separate key to
give you the reciprocal of any number in
its display.
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Powers And Roots In Base Ten
To raise a power of ten to a power simply
multiply the exponents.
 To find the square root of a number, raise
that number to the 1/2 power.
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