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.