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Exponents and Scientific Notation

Exponents and Scientific Notation. Method of writing very large or very small numbers to make mathematical manipulations easier Numbers are expressed as some quantity between 1 & 10 multiplied by 10 raised to some exponent N = A x 10. n.

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Exponents and Scientific Notation

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  1. Exponents and Scientific Notation • Method of writing very large or very small numbers to make mathematical manipulations easier • Numbers are expressed as some quantity between 1 & 10 multiplied by 10 raised to some exponent N = A x 10 n

  2. Every non-zero number can be written in scientific notation. • For example

  3. More examples The speed of light it approx. 30,000,000,000 cm/s in scientific notation we would move the decimal 10 places to the left and would express the number as 3 x 1010 cm/s (only sig figs are expressed)

  4. The diameter of an atom = 0.0000000001m In scientific notation we would move the decimal place 10 places to the right and the measurement would be expressed as 1 x 10-10 m

  5. Parts of a number in scientific notation A x 10n A = coefficient between 1 & 9, can be positive or negative (must be ≥ 1 and < 10) 10 = called the base n = integer, positive, negative or zero

  6. Converting to Scientific Notation For numbers 10 or greater • 1 . To find “A” - move decimal point to the left until one digit remains to the left of the decimal point • To find “n” count how many places you moved the decimal • 456,000 = 4.56 x 10 5 • “n” is positive if – • you moved the decimal to the left • if the number in decimal form was greater than 10

  7. Converting to Scientific Notation For numbers less than 1 • 1 . To find “A” - move decimal point to the right until one digit remains to the right of the decimal point • To find “n” count how many places you moved the decimal • 0.0000456 = 4.56 x 10 -5 • “n” is negative if – • you moved the decimal to the right • if the number in decimal form was less than 1

  8. Numbers 1 – 9.999999 • No conversion is necessary • Written as A x 100 (100 = 1) 3.45 to scientific notation 3.45 = 3.45 x 100

  9. Convert from Decimal form to Scientific Notation (a) 93,000,000 (b) .00005144 (c) -33,452.8

  10. Convert from Scientific Notation to Decimal Form

  11. Watch the zeros! 0.000068120 m (5 sig figs) = 6.8120 x 10-5 0.006060 g (4 sig figs) = 6.060 x 10-3 52.0030 L (6 sig figs) = 5.20030 x 101 676.0 cm (4 sig figs) = 6.760 x 102

  12. Double check!! Correct way to write: 5.533 x 10 5 Incorrect way to write: 55.33 x 10 5 Do in class exercises

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