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. General formula: (N X 10x) (M X 10y) = (N) (M) X 10x+y

Example 1 Given: 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

Given: (2.93 X 10-2) • (8.3 X 10-5) Example 2 Multiply Decimals: 2.93 X 8.3 = 24.319 Add Exponents: 10-2 x 10-5=10-2+(-5)=10-7 Answer: 24.319 X 10-7 Rewrite in Scientific Notation Final Answer: 2.43 X 10-6

Dividing Numbers in Scientific Notation Divide the decimal numbers. Then subtract the exponents General formula:

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

Example 2 Given: 3.45 X 102 1.23 X 10-5 Divide decimals: 3.45 ÷ 1.23= 2.81 Subtract exponents: 2- -5 =7 Answer: 2.81 X 107

Practice Quiz Questions 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 = ?