Scientific Notation Multiplication and Division Guide
Learn how to multiply and divide numbers in scientific notation with step-by-step examples. Understand the process of multiplying decimals, adding exponents, dividing, and converting to proper scientific notation. Practice various scenarios to master these mathematical operations.
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Multiplying and Dividing in Scientific Notation
Multiplying Numbers in Scientific Notation Multiply the decimal numbers together. Add the exponents to get the power of 10. Sometimes, you might have to adjust it so that the answer is in proper scientific notation. General formula: (a X 10x) (b X 10y) = (ab) X 10x+y
Example 1 3.42 X 105 4.67 X 109 Multiply decimals: 3.42 X 4.67 = 15.97 Add Exponents: 105x 109=105+9= 1014 Preliminary Answer: 15.97 X 1014 Now, Rewrite in Scientific Notation if needed. Final Answer: 1.597 X 1015
Example 2 (2.93 X 10-2) (8.3 X 10-5) (2.93 X 8.3)(10-2x 10-5) 24.319 X 10-7 Final Answer: 2.43 X 10-6 End of X
Dividing Numbers in Scientific Notation Divide the decimal numbers. Then subtract the exponents x N 10 N M General formula: x y = 10 y M 10
Example 1 Given: 8 x x 10-3 2 x x 10-2 Divide decimals: 8 2 = 4 Subtract exponents: (-3)-(-2)= -1 4 x 10-1 Final Answer:
Example 2 Given: 3.45 X 102 1.23 X 10-5 (3.45 1.23)(102 10-5)= 2.81 X 107
Review/Extended Questions Question 1 Write these 2 numbers in scientific notation: 0.000467 32000000 Question 2 Express 5.43 x 10-3 in standard form Question 3 (4.5 x 10-14) x (5.2 x 103) = ? (6.1 x 105)/(1.2 x 10-3) = ? Question 4 Question 5 (3.74 x 10-3)4 = ?
