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Scientific notation What is scientific notation? Numbers are written in the form M × 10 ^n, Where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number. Ex. 6.5 × 10⁴ km Ex. 9.8 × 10¯³ g How to determine scientific notation Determine M by moving the decimal point in the original number to the left or right so that only one nonzero digit remains to the left of the decimal point. Ex. 34000 = 3.4 × 104 Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it to the right, n is negative. Ex. 450 = 4.5 × 10² Ex. .00091 = 9.1 × 10¯⁴ Convert numbers into scientific notation 89000 68.65 .00087 .000000000453 222.22 Adding and subtracting scientific notation Can be performed only if the values have the same exponent (n factor). Ex. 4.2 × 10² − 2.2 × 10² = 2 × 10² If they do not have the same number, adjustments must be made so the exponent values are equal. Ex. 7.001 × 10³ + 9.3 × 10⁴ = .7001 × 10⁴ + 9.3 × 10⁴ = 10.0001 × 10⁴ = 1.00001 × 10⁵ Add or subtract 6.09 × 10¯¹ + 9.2 × 10¯¹ 7.968 × 10⁴ - 9.68 × 10³ 5900 + 7.8 × 10³ 2.31 × 10¯³ + 6.12 × 10¯⁵ 1.22 × 10¹² + 1.22 × 10¹⁴ 2.34 × 10² + 1.8 × 10¯¹ Multiplication of scientific notation The M factors are multiplied, and the exponents are added algebraically. Ex. 1.2 × 10⁵ × 5.45 × 10² = 6.54 × 10⁷ Multiply scientific notations 7.8 X 107 X 1.2 X 105 6.3 X 10−3 X 7.0 X 105 6.12 X 103 X 2.1 X 10−23 6.022 X 1023 X 5.01 X 102 7.32 X 1.5 X 104 Dividing scientific notation The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. Ex. 5.44 x 107 ÷ 8.1 × 104 = 0.67 x 103 = 6.7 x 102 Divide scientific notations 9.4× 109 ÷ 3.54 × 102 6.32× 107 ÷ 7.55 × 10−2 8.655× 10−9 ÷ 5.12 × 108 6.54 ÷ 8.66 × 10−7 8.22 × 102 ÷ 6.022 × 1023