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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

Powers of Ten (cont.)

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

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.

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

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

Division In Powers Of Ten Form

- Division of numbers containing powers of ten

involves subtraction of the exponents. - 103/102 101

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.

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.

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.

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.

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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