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Scientific Notation

Multiplication and Division in Scientific Notation

Problems

Problems

Multiplication and Division

Quantities with exponents can be multiplied and divided easily if they have the same base. Since all number in scientific notation have base 10 , we can always multiply them and divide them.

To multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation.

Here are the steps to multiply two numbers in scientific notation:

  1. Multiply the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.
  2. Add the exponents.
  3. Convert the result to scientific notation.

Here are the steps to divide two numbers in scientific notation:

  1. Divide the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.
  2. Subtract the exponents.
  3. Convert the result to scientific notation.

Example 1: (5.60×1012)×(7.102×104) = ?

  1. 5.6×7.102 = 39.8
  2. 1012×104 = 1012+4 = 1016
    (5.60×1012)×(7.102×104) = 39.8×1016
  3. 39.8×1016 = 3.98×1017


Thus, (5.6×1012)×(7.102×104) = 3.98×1017 .

Example 2: (3.04×105)÷(9.89×102) = ?

  1. = 0.307
  2. = 105-2 = 103
    (3.04×105)÷(9.89×102) = 0.307×103
  3. 0.307×103 = 3.07×102
Thus, (3.04×105)÷(9.89×102) = 3.07×102 .

Example 3: (5.3201×10-5)×(1.8×103) = ?

  1. 5.3201×1.8 = 9.6
  2. 10-5×103 = 10-5+3 = 10-2
    (5.3201×10-5)×(1.8×103) = 9.6×10-2
  3. 9.6×10-2 is in scientific notation.
Thus, (5.3201×10-5)×(1.8×103) = 9.6×10-2 .

Example 4: (4.14×10-4)÷(8.28×100) = ?

  1. = 0.500
  2. = 10-4-0 = 10-4
    (4.14×10-4)÷(8.28×100) = 0.500×10-4
  3. 0.500×10-4 = 5.00×10-5
Thus, (4.14×10-4)÷(8.28×100) = 5.00×10-5 .

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