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Scientific Notation. 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
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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 0.000005789; 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?
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
No Yes Yes Yes No No Pop Quiz N x 10X • Are the following numbers written in scientific notation? 4.8756 x 1000 .01867x109 2.37895 x 102 22.479x10-4 239 x 1004 9.74 x 104,660
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 theleft of its original, the exponent is treated as positive If the new position of the decimal point is to therightof its original, the exponent is negative Converting Standard Form to Scientific Notation N x 10X
Examples N x 10X • Converting standard form to scientific notation 248 = 2.48x102 0.0000547 = 5.47x10-5 0.0348987 = 3.48987x10-2 4,378,000,000 = 4.378x109 314,150,000,000,000 = 31.415x1013
Notice two things: The location of the decimal point in themantissa The sign of theexponent 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 Converting Scientific Notation to Standard Form N x 10X
Examples N x 10X • Converting scientific notation to standard form 3.086x106 = 3,086,000 547x10-4 = .0547 5.8756x102 = 587.56 43.995005x1010 = 439,950,050,000 .5x101 = 5
