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MULTIPLICATION AND DIVISION IN SCIENTIFIC NOTATION Part 2: How Do we Divide numbers in Scientific Notation? Scientific Notation is based on powers of the base number 10. The number 123,000,000,000 in scientific notation is written as : 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 base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten. Rules for Division in Scientific Notation: 1) Divide the coefficients 2) Subtract the exponents (base 10 remains) Example 1: (6 x 106) / (2 x 103) = 3 x 103 What happens if the coefficient is less than 10? Example 2: (2 x 10 7) / (8 x 103) = 0.25 x 104 While the value is correct it is not correctly written in scientific notation since the coefficient is not between 1 and 10. We must move the decimal point over to the right until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be lowered 1 power of ten. 0.25x10 4 = 2.5 x 103 in scientific notation. Now Try these: (write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 3 you should type 3.5x10^3 in the box then click the submit button). (4 X 106) / (2X104)= (9 X 108) / (2 X 10 6)= (3 X 107) / (8 x 104)= What happens when the exponent(s) are negative?We still subtract the exponents (apply the rules for subtracting signed numbers)Example 5: (9 x 10 -6) / (3x 10-3) = 3. x 10-3 Example 6: (2 x 10 3) / (4 x 10-8) = 0.5 x 1011 = 5 x 10 10Now Try these: (write your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10 3 you should type 3.5x10^3 in the box then click the submit button).   (3 X 10-6) / (2X10-4)= (7 X 10-5 ) / (2 X 10 10)= (1.5 X 10-7) / (3.0 x 104)= (3 X 107) / (8 x 10-6) =  Go to Word Problems Using Scientific Notation
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