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Powers of Ten

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

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Powers of Ten

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  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.

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