 Scientific notation is a way of expressing really big numbers or really small numbers.  It is most often used in “scientific” calculations where the analysis must be very precise.

 For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.  Numbers expressed in scientific notation makes it easier to solve problems with big and small numbers.

 A number between 1 and 10  A power of 10 N x 10 x Are the following in scientific notation?

 Place the decimal point so that there is one non-zero digit to the left of the decimal point.  Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

 If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

See if the original number is greater than or less than one. › If the number is greater than one, the exponent will be positive = x 10 5 › If the number is less than one, the exponent will be negative = 6.72 x 10 -8

Positive Exponent: 2.35 x 10 8 Negative Exponent: 3.97 x 10 -7

93,000,000

 Move decimal left  Leave only one number in front of decimal

 Write number without zeros

 Count how many places you moved decimal  Make that your power of ten

The power of ten is 7 because the decimal moved 7 places.

 93,000, Standard Form  9.3 x Scientific Notation

1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten x x x x 10 6

1) 734,000,000 = ______ x ) 870,000,000,000 = ______x ) 90,000,000,000 = _____ x On these, decide where the decimal will be moved. 1)7.34 x ) 8.7 x ) 9 x 10 10

1) 50,000 2) 7,200,000 3) 802,000,000,000 Write in scientific notation. 1) 5 x ) 7.2 x ) 8.02 x 10 11

 Given: 289,800,000  Use: (moved 8 places)  Answer: x 10 8

 Given:  Use: 5.67 (moved 4 places)  Answer: 5.67 x 10 -4

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1) ) ) ) x x x x 10 3

 Move the decimal point to the right for positive exponent 10.  Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

 If an exponent is positive, the number gets larger, so move the decimal to the right.  If an exponent is negative, the number gets smaller, so move the decimal to the left.

Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form move the decimal

 Given: x 10 6  Answer: 5,093,000 (moved 6 places to the right)

 Given: x  Answer: (moved 4 places to the left)

 6.27 x 10 6  9.01 x 10 4  6,270,000  90,100

1) x ) x ) x ) x

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