SCIENTIFIC NOTATION Writing Numbers That Are Too Big

SCIENTIFIC NOTATION Writing Numbers That Are Too Big or Too Small in Decimal Form

Definitions • Scientific Notation o A number between one and ten, including one, multiplied by a power of ten. • Power of Ten o A product of multiplying ten by itself one or more times. • Negative Exponent o The opposite of a power of a number; used to express smaller numbers.

Standard Notation to Scientific Notation •

Steps Write 312, 000, 000 in Scientific Notation. • Step One o Move the decimal place to the left to create a new number from 1 up to 9. o o Where is the decimal point in 312, 000, 000? Because this is a whole number, the decimal point is understood to be at the end of the number: 312, 000, 000 Decimal Point

Steps • 312, 000, 000 o becomes 3 12 • Step Two o Drop all zeros • Step Three Count the number of places from the old decimal point to the new decimal point. o In this case, there are 11 places. o

Steps •

Practice •

Scientific Notation to Standard Notation •

Practice • 6, 806, 000 4, 000 2, 000 310, 400, 000

Mixed Review • 2, 612, 000 30, 600 61, 028, 000

Practice •

Practice

Negative Exponents 10000 = 10 x 10 = 104 1000 = 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 • Do you see a pattern? • Can you guess what the next exponent will be?

Negative Exponents = 1 = = = = 10 -4

Practice • Rewrite the following decimals with negative exponents. • 0. 00082 o 8. 2 X 10 -4 • 0. 00000059 o 5. 9 X 10 -7 • 0. 00004 o 4 X 10 -5

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Practice •

Practice •