2 What is Scientific Notation? Scientific notation is a way of writing numbersIt is very convenient to express numbers that are too large or too small to be written in decimal form in a simpler wayTry 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 mannerWhy would it be beneficial to write numbers in scientific notation?When do you use very large or very small numbers anyway?
3 Two Parts to Scientific Notation Numbers written in scientific notation look like to following:N x 10XRead 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 numberX, which is called the “Exponent”X MUST be an integer
4 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?NoYesx 1000.01867x109YesNox 10222.479x10-4239 x 10049.74 x 104,660
5 Converting Standard Form to Scientific Notation N x 10XPut the decimal point after the first, second, or third digit.The leftmost digit should always be between 1-9; it CANNOT be a ZEROCount the number of places that the decimal point was moved from its original location. This number will be your exponentIf the new position of the decimal point is to the left of its original, the exponent is treated as positiveIf the new position of the decimal point is to the right of its original, the exponent is negative
6 ExamplesN x 10XConverting standard form to scientific notation248 = 2.48x102= 5.47x10-5= x10-24,378,000,000 = 4.378x109314,150,000,000,000 = x1013
7 Converting Scientific Notation to Standard Form N x 10XNotice two things:The location of the decimal point in the mantissaThe sign of the exponentIf the sign of the exponent is positive, move the decimal point in the mantissa X digits to the rightIf the sign of the exponent is negative, move the decimal point in the mantissa X digits to the leftFill in any empty spaces between the last number in the mantissa and the new position of the decimal point with ZEROS
8 ExamplesN x 10XConverting scientific notation to standard form3.086x106 = 3,086,000547x10-4 = .05475.8756x102 =x1010 = 439,950,050,000.5x101 = 5