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Scientific Notation

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**What is Scientific Notation?**

Scientific notation is a way of writing numbers It is very convenient to express numbers that are too large or too small to be written in decimal form in a simpler way Try multiplying 1,234,000,000,000 by ; is there an easy way to write the result? Scientific notation allows us to write and handle numbers in a concise manner Why would it be beneficial to write numbers in scientific notation? When do you use very large or very small numbers anyway?

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**Two Parts to Scientific Notation**

Numbers written in scientific notation look like to following: N x 10X Read it as “N times TEN to the power of X” Notice that there are two main components: N, which is called the “Mantissa” N can be any number X, which is called the “Exponent” X MUST be an integer

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**Pop Quiz N x 10X No Yes 4.8756 x 1000 .01867x109 Yes No 2.37895 x 102**

Are the following numbers written in scientific notation? No Yes x 1000 .01867x109 Yes No x 102 22.479x10-4 239 x 1004 9.74 x 104,660

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**Converting Standard Form to Scientific Notation**

N x 10X Put the decimal point after the first, second, or third digit. The leftmost digit should always be between 1-9; it CANNOT be a ZERO Count the number of places that the decimal point was moved from its original location. This number will be your exponent If the new position of the decimal point is to the left of its original, the exponent is treated as positive If the new position of the decimal point is to the right of its original, the exponent is negative

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Examples N x 10X Converting standard form to scientific notation 248 = 2.48x102 = 5.47x10-5 = x10-2 4,378,000,000 = 4.378x109 314,150,000,000,000 = x1013

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**Converting Scientific Notation to Standard Form**

N x 10X Notice two things: The location of the decimal point in the mantissa The sign of the exponent If the sign of the exponent is positive, move the decimal point in the mantissa X digits to the right If the sign of the exponent is negative, move the decimal point in the mantissa X digits to the left Fill in any empty spaces between the last number in the mantissa and the new position of the decimal point with ZEROS

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Examples N x 10X Converting scientific notation to standard form 3.086x106 = 3,086,000 547x10-4 = .0547 5.8756x102 = x1010 = 439,950,050,000 .5x101 = 5

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