Multiplying and Dividing in Scientific Notation Multiplying Numbers

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 10 x) (b X 10 y) = (ab) X 10 x+y

Example 1 3. 42 X 105 • 4. 67 X 109 • • Multiply decimals: 3. 42 X 4. 67 = 15. 97 Add Exponents: 105 x 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 -2 x 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 • General formula:

Example 1 • Given: 8 x 10 -3 2 x 10 -2 • Divide decimals: 8÷ 2 = 4 • Subtract exponents: (-3)-(-2)= -1 • Final Answer: 4 x 10 -1

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) = ? Question 4 (6. 1 x 105)/(1. 2 x 10 -3) = ? Question 5 (3. 74 x 10 -3)4 = ?