Presentation on theme: "Scientific Notation Scientific notation is used when numbers are either very large or very small Standard Notation Scientific Notation Measurement 300,000,000."— Presentation transcript:
1 Scientific NotationScientific notation is used when numbers are either very large or very smallStandard NotationScientific NotationMeasurement300,000,000 m/sec3.00×108 m/sspeed of light kg×10−31 kgmass of electron kg1.6726×10−27 kgmass of proton kg5.9736×1024 kgmass of Earthkg7.53×10−10 kgmass of a dust particle m (40 Mm)4×107 mcircumference of Earthkmx1012 kmone light year
2 Scientific Notation is based on powers of the base number 10 The number 123,000,000,000 in scientific notation is written as:𝟏.𝟐𝟑 𝒙 𝟏𝟎 𝟏𝟏The first number, 1.23, is called the coefficient. It must be greater than or equal to 1 and less than 10.The second number is called the base. It must always be 10 in scientific notation.The number 11 is referred to as the exponent.
3 Converting from Standard Form to Scientific Notation Place the decimal point to the right of the first non-zero digit.Count the number of decimal places the decimal has "moved" from the original number. This will be the exponent of the 10.If the original number was less than 1, the exponent is negative;If the original number was greater than 1, the exponent is positive.
4 Examples:Given: (moved decimal point 6 decimal places)Answer: 4.75 X 106The original number was greater than 1 so the exponent is positiveGiven: 7.89 (moved decimal point 4 decimal places)Answer: 7.89 X 10-4The original number was less than 1 so the exponent is negative
5 Converting from Scientific Notation to Standard Form Move the decimal point to the right for positive exponents of 10. The exponent tells you how many places to move. Move the decimal point to the left for negative exponents of 10. The exponent tells you how many places to move.
6 Examples:Given: x 10-8Negative exponents move decimal to the leftAnswer: Given: x 103Positive exponents move decimal to the rightAnswer: 5024
7 Try working on Practice Questions … Scientific NotationEx) Convert the following to scientific notation:(a) = ______________________(b) = ____________________5.3 x 10-54.0 x 107Try working on Practice Questions …Express the following numbers in scientific notation:= _________________________= _________________________58.23 = _________________________= _________________________12452 = _________________________1.003 x 10123.998 x 10-105.823 x 1012.038 x 10-1x 104
8 For the following use the exponent button on your calculator 2. Express the following numbers to decimal notation:1.77 x 107 = ________________________2.552 x 10-9 = _________________________1.18 x 103 = _________________________4.44 x 10-1 = _________________________1.399 x 100 = _________________________11800.4441.399For the following use the exponent button on your calculatorEXP, E, EE, x10x3. Express the results of the following operations in scientific notation:1.39 x x 10-4 = _________________________1.17 x x 102 = _________________________(1.81 x 10-3) (1.06 x 1020) = _________________________(5.77 x 10-4) (1.71 x 10-11) = _________________________1.42 x 10-21.13 x 1041.92 x 10173.37 x 107