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

How to do calculations on your scientific calculator 1. Make sure that the number in scientific notation is put into your calculator correctly. 2. Read the directions for your particular calculator. For basic scientific calculators: Punch the number (the decimal number) into your calculator. Push the EE or EXP button. Do NOT use the x (times) button!! Enter the exponent number. Use the +/- button to change its sign. Voila! To check yourself: multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x 109.

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 = ?