Scientific Notation Scientific notation is used when numbers are either very large or very small Standard Notation Scientific Notation Measurement 300,000,000 m/sec 3.00×108 m/s speed of light 0.00000000000000000000000000000091093822 kg 9.1093822×10−31 kg mass of electron 0.0000000000000000000000000016726 kg 1.6726×10−27 kg mass of proton 5973600000000000000000000 kg 5.9736×1024 kg mass of Earth 0.000 000 000 753 kg 7.53×10−10 kg mass of a dust particle 40000000 m (40 Mm) 4×107 m circumference of Earth 9 460 528 400 000 km 9.4605284x1012 km one light year

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 𝟏𝟏 The 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.

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.

Examples: Given: 4 750 000 4.750 000 (moved decimal point 6 decimal places) Answer:  4.75 X 106 The original number was greater than 1 so the exponent is positive Given:  0.000789 7.89 (moved decimal point 4 decimal places) Answer:  7.89 X 10-4 The original number was less than 1 so the exponent is negative

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.

Examples: Given:  1.015 x 10-8 Negative exponents move decimal to the left Answer:  0.00000001015  Given:  5.024 x 103 Positive exponents move decimal to the right Answer:  5024

Try working on Practice Questions … Scientific Notation Ex) Convert the following to scientific notation: (a) 0.000053 = ______________________ (b) 40 000 000 = ____________________ 5.3 x 10-5 4.0 x 107 Try working on Practice Questions … Express the following numbers in scientific notation: 1003000000000 = _________________________ 0.0000000003998 = _________________________ 58.23 = _________________________ 0.2038 = _________________________ 12452 = _________________________ 1.003 x 1012 3.998 x 10-10 5.823 x 101 2.038 x 10-1 1.2452 x 104

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 = _________________________ 17700000 0.000000002552 1180 0.444 1.399 For the following use the exponent button on your calculator EXP, E, EE, x10x 3. Express the results of the following operations in scientific notation: 1.39 x 10-2 + 3.11 x 10-4 = _________________________ 1.17 x 104 - 3.57 x 102 = _________________________ (1.81 x 10-3) (1.06 x 1020) = _________________________ (5.77 x 10-4)  (1.71 x 10-11) = _________________________ 1.42 x 10-2 1.13 x 104 1.92 x 1017 3.37 x 107