Powers of Ten

1
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

2
Powers of Ten (cont.)

• Problems With Complex Denominators Or Numerators
• Reciprocals
• Powers And Roots In Base Ten

3
Positive Exponents

• 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.

4
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

5
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

6
Division In Powers Of Ten Form

• Division of numbers containing powers of ten
  involves subtraction of the exponents.
• 103/102 101

7
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.

8
Scientific Notation

• 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.

9
Problems With Complex Denominators Or Numerators

• 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.

10
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.

11
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.