Scientific Notation
Scientific Notation
Slide: 1
Section 2.1
Scientific Notation Scientific notation is a method of expressing very large or very small numbers as a decimal number multiplied by a power of 10.
Exponent
7
73,400,000 = 7.34 × 10 The base is always 10, and the coefficient should be greater than or equal to 1 and less than 10.
Slide: 2
Coefficient
Base
Convert the following numbers to scientific notation: 1. 2. 3.
Move the decimal point to the left (large number) or right (small number) until only 1 non-zero digit is to the left of it. Drop all trailing and leading zeros. The exponent is equal to the number of places the decimal point moved: • If the decimal moved left, the exponent is positive. • If the decimal moves right, the exponent is negative.
180,000 = 0.00906 = Slide: 3
Convert the following numbers to scientific notation: 2.6567 × 108 a. b. c. d.
Slide: 4
0.000000026567 0.00026567 265,670,000 26,567,000
Convert the following numbers to scientific notation: 2.6567 × 108
Slide: 5
Addition and Subtraction of Numbers in Scientific Notation To add or subtract numbers in scientific notation whose exponents are the same, factor out the exponent and add or subtract the numbers within the brackets.
3.24 × 105 + 6.08 × 105 = (3.24 + 6.08) × 105 5 = 9.32 × 10 Slide: 6
Addition and Subtraction of Numbers in Scientific Notation To add or subtract numbers in scientific notation whose exponents are different, they must be converted to have the same exponent.
5.3 ×
7 10
+ 3.1 ×
8 10
Determine the number by which the smaller exponent needs to be increased to make it equal to the larger exponent. 8 Increase the smaller number by this number and move the decimal point of the coefficient of the number to the left by the same number of places.
= 5.3 × 10(7+1) + 3.1 × 10 = 0.53 × 108 + 4.1 × 108 = (0.53 + 4.1) × 108 Add the coefficients and factor out the common exponent in power of 10. = 4.63 × 108
Slide: 7
Subtract the following numbers: 4.47 × 10–5 – 3.11 × 10–6 a. b. c. d.
Slide: 8
–2.663 × 10–6 4.159 × 10–5 1.36 × 10–6 1.36 × 10–5
Subtract the following numbers: 4.47 × 10–5 – 3.11 × 10–6
Slide: 9
Multiplication of Numbers in Scientific Notation To multiply numbers in scientific notation, simply multiply their coefficients and add their exponents.
5 10 )
(5.54 × × (8.1 × = (5.54 × 8.1) × 10[5 + (–12)] = 44.874 × 10–7 If your coefficient is less than 1 or greater than or equal to 10, make sure to convert your answer back = 4.4874 × 10–6 to scientific notation. Slide: 10
–12 10 )
Division of Numbers in Scientific Notation To divide numbers in scientific notation, simply divide their coefficients and subtract their exponents.
(2.40 × 103) ÷ (6.25 × 10–7) [3 – (–7)] = (2.40 ÷ 6.25) × 10 10 = 0.384 × 10 9 = 3.84 × 10 Slide: 11
Divide the following numbers: 6.44 × 1010 ÷ 3.2 × 105 a. b. c. d.
Slide: 12
2.0125 × 102 2.0125 × 105 20.125 × 101 20.125 × 104
Divide the following numbers: 6.44 × 1010 ÷ 3.2 × 105
Slide: 13
Solve the following equation by first converting the numbers to scientific notation. Round the coefficient to one decimal place. !.!!!!!!#!$%!.!!!!!&'( = )*,#!!,!!!×!.!!!*'
Slide: 14
Slide: 1
Section 2.1
Scientific Notation Scientific notation is a method of expressing very large or very small numbers as a decimal number multiplied by a power of 10.
Exponent
7
73,400,000 = 7.34 × 10 The base is always 10, and the coefficient should be greater than or equal to 1 and less than 10.
Slide: 2
Coefficient
Base
Convert the following numbers to scientific notation: 1. 2. 3.
Move the decimal point to the left (large number) or right (small number) until only 1 non-zero digit is to the left of it. Drop all trailing and leading zeros. The exponent is equal to the number of places the decimal point moved: • If the decimal moved left, the exponent is positive. • If the decimal moves right, the exponent is negative.
180,000 = 0.00906 = Slide: 3
Convert the following numbers to scientific notation: 2.6567 × 108 a. b. c. d.
Slide: 4
0.000000026567 0.00026567 265,670,000 26,567,000
Convert the following numbers to scientific notation: 2.6567 × 108
Slide: 5
Addition and Subtraction of Numbers in Scientific Notation To add or subtract numbers in scientific notation whose exponents are the same, factor out the exponent and add or subtract the numbers within the brackets.
3.24 × 105 + 6.08 × 105 = (3.24 + 6.08) × 105 5 = 9.32 × 10 Slide: 6
Addition and Subtraction of Numbers in Scientific Notation To add or subtract numbers in scientific notation whose exponents are different, they must be converted to have the same exponent.
5.3 ×
7 10
+ 3.1 ×
8 10
Determine the number by which the smaller exponent needs to be increased to make it equal to the larger exponent. 8 Increase the smaller number by this number and move the decimal point of the coefficient of the number to the left by the same number of places.
= 5.3 × 10(7+1) + 3.1 × 10 = 0.53 × 108 + 4.1 × 108 = (0.53 + 4.1) × 108 Add the coefficients and factor out the common exponent in power of 10. = 4.63 × 108
Slide: 7
Subtract the following numbers: 4.47 × 10–5 – 3.11 × 10–6 a. b. c. d.
Slide: 8
–2.663 × 10–6 4.159 × 10–5 1.36 × 10–6 1.36 × 10–5
Subtract the following numbers: 4.47 × 10–5 – 3.11 × 10–6
Slide: 9
Multiplication of Numbers in Scientific Notation To multiply numbers in scientific notation, simply multiply their coefficients and add their exponents.
5 10 )
(5.54 × × (8.1 × = (5.54 × 8.1) × 10[5 + (–12)] = 44.874 × 10–7 If your coefficient is less than 1 or greater than or equal to 10, make sure to convert your answer back = 4.4874 × 10–6 to scientific notation. Slide: 10
–12 10 )
Division of Numbers in Scientific Notation To divide numbers in scientific notation, simply divide their coefficients and subtract their exponents.
(2.40 × 103) ÷ (6.25 × 10–7) [3 – (–7)] = (2.40 ÷ 6.25) × 10 10 = 0.384 × 10 9 = 3.84 × 10 Slide: 11
Divide the following numbers: 6.44 × 1010 ÷ 3.2 × 105 a. b. c. d.
Slide: 12
2.0125 × 102 2.0125 × 105 20.125 × 101 20.125 × 104
Divide the following numbers: 6.44 × 1010 ÷ 3.2 × 105
Slide: 13
Solve the following equation by first converting the numbers to scientific notation. Round the coefficient to one decimal place. !.!!!!!!#!$%!.!!!!!&'( = )*,#!!,!!!×!.!!!*'
Slide: 14
