ELEC 103 Scientific Notation24 September 2005 1ELEC 103Scientific Notation24 September 2005 ELEC 103 - Scientific Notation 2ObjectiveAt the conclusion of this presentation the student will:• Describe the purpose of Scientific Notation and Engineering Notation• Convert numbers from floating point notation to scientific notation, and from scientific notation to floating point notation • Convert numeric values between floating point notation and engineering notation• Use prefixes with units of measurement• Perform calculations with scientific notation, engineering notation, and prefixes with units of measurementELEC 103 Scientific Notation24 September 2005 224 September 2005 ELEC 103 - Scientific Notation 3Purpose of Scientific Notation• Before calculators existed, engineers, scientists, and technicians would perform calculations on a slide rule• When using this tool, it was necessary to use scientific notation to keep track of the powers of ten that occurred.• It is also necessary because we regularly must work with very large or very small numbers– The charge of 1 electron is 1.602 x 10-19C or.000 000 000 000 000 000 016 02 C– There are 6.242 x 1018electrons in 1 C of charge or6 242 000 000 000 000 000 e-24 September 2005 ELEC 103 - Scientific Notation 4Purpose of Scientific Notation• When recording these very large and small values, it is easy to add or miss one or more of the values• Most scientific calculators only have 10 to 15 digits to display numeric data– Very large and very small numeric data must be entered in scientific notation• When using scientific notation or engineering notation, we usually round numeric data to a specific number of significant digitsELEC 103 Scientific Notation24 September 2005 324 September 2005 ELEC 103 - Scientific Notation 5Rounding Numeric Data• When using scientific and engineering notation, it is necessary to round the numeric values.• Significant digits– Digits from 1-9 are always significant– Zeros between two other non-zero digits are always significant – Zeros used solely for spacing the decimal point (placeholders) are not significant• When rounding numeric data, use the following rules:– Determine the number of significant digits you wish to have in the rounded value– Look at the digit to the right of the least significant digit– If it is less than 5, round down– If it is more than 5, round up– If it is exactly 5, round s the least significant digit is even24 September 2005 ELEC 103 - Scientific Notation 6Purpose of Scientific Notation• Scientific notation was developed to solve the problem of writing very large and small numbers• Numbers written in scientific notation have two parts: a numeric value, which is a number between 1 and 9.9, times 10 raised to a power93,000,000 = 9.3 x 107Numeric Value Power of 10ELEC 103 Scientific Notation24 September 2005 424 September 2005 ELEC 103 - Scientific Notation 7Scientific Notation• Which numbers below are written in scientific notation?17.45 x 10-61.745 x 10-60.1745 x 10-63.6 x 10936 x 109.36 x 10924 September 2005 ELEC 103 - Scientific Notation 8Scientific Notation• Which numbers below are written in scientific notation?17.45 x 10-61.745 x 10-60.1745 x 10-63.6 x 10936 x 109.36 x 109ELEC 103 Scientific Notation24 September 2005 524 September 2005 ELEC 103 - Scientific Notation 9Purpose of Scientific Notation• Multiplying by a multiple of ten can be done by moving the decimal.• The exponent on the “power of ten” tells how many places to move the decimal.• The “power of ten” part of a number in scientific notation is a multiple of 10.93,000,000 = 9.3 x 107107= 10,000,0009 3,000,000.7 places9.3 x 10 724 September 2005 ELEC 103 - Scientific Notation 10Purpose of Scientific Notation• Which number below is written in scientific notation?Α 8.5 x 10 4is the only number that is written strictly in scientific notation because the base must be less than 10. – 1.82 x 610– 8.5 x 104– 3.1 x 1006ELEC 103 Scientific Notation24 September 2005 624 September 2005 ELEC 103 - Scientific Notation 11Convert to Scientific Notation • Write 8,760,000,000 in scientific notation.• Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.8 7 6 0 0 0 0 0 0 0..8.76 is the Numeric Value24 September 2005 ELEC 103 - Scientific Notation 12Convert to Scientific Notation • Write 8,760,000,000 in scientific notation.• Step 2: The number of places you moved the decimal will be the exponent on the power of 108 7 6 0 0 0 0 0 0 0..8.76 is the Numeric Value9 places10 9is the Power of 10ELEC 103 Scientific Notation24 September 2005 724 September 2005 ELEC 103 - Scientific Notation 13Convert to Scientific Notation • Write 8,760,000,000 in scientific notation.• Step 3: Write the number so it is the stem times the power of ten.8 7 6 0 0 0 0 0 0 0..9 places10 9is the Power of 108.76 x 10 9= 8,760,000,0008.76 is the Numeric Value24 September 2005 ELEC 103 - Scientific Notation 14Convert to Scientific Notation • Write the following numbers in scientific notation660,000,000 =90300 =397 =4,500,000 =8,000,100,000 =159,400 =7,300 =ELEC 103 Scientific Notation24 September 2005 824 September 2005 ELEC 103 - Scientific Notation 15Convert to Scientific Notation • There are two differences when writing a small number in scientific notation.• First, the decimal is moved in the opposite direction• Second, the exponent is negative24 September 2005 ELEC 103 - Scientific Notation 16Convert to Scientific Notation • Write 0.00000000482 in scientific notation.• Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.0 0 0 0 0 0 0 0 0 4. 8 2.4.82 is the Numeric ValueELEC 103 Scientific Notation24 September 2005 924 September 2005 ELEC 103 - Scientific Notation 17Convert to Scientific Notation • Write 0.00000000482 in scientific notation.0 0 0 0 0 0 0 0 0 4 8 2..4.82 is the numeric value• Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1.9 places10 -9is the Power of 1024 September 2005 ELEC 103 - Scientific Notation 18Convert to Scientific Notation • Write 0.00000000482 in scientific notation.0 0 0 0 0 0 0 0 0 4 8 2..4.82 is the numeric value• Step 3: Write the number so it is the numeric value times the power of ten.9 places10 -9is