Multiplying and Dividing in Scientific Notation

Multiplying Numbers in Scientific Notation Multiply the base numbers together. Then add the exponents. 5.1 x 103 • 1.0 x 104 =

Example 1 Given: (3.42 X 105)(4.67 X 109) Multiply bases: 3.42 X 4.67 = 15.97 Add Exponents: 105+109=105+9=1014 Answer: 15.97 X 1014 Shift Decimal left one place. Final Answer: 1.597 X 1014

Example 2 Given: (2.93 X 10-2)(8.3 X 10-5) Multiply Bases: 2.93 X 8.3 = 24.319 Add Exponents: 10-2+10-5=10-2+(-5)=10-7 Answer: 24.319 X 10-7 Shift decimal left one place. Final Answer: 2.43 X 10-6

Dividing Numbers in Scientific Notation Divide the base numbers. Then subtract the exponents. (6.6 x 106) ÷ (2.0 x 104) =

Example 1 Given:8 X 10-3 / 2 X 10-2 Divide bases: 8/2=4 Subtract exponents: (-3)-(-2)=-1 Answer: 4 X 10-1

Example 2 Given:3.45 X 102 / 1.23 X 10-5 Divide bases: 3.45/1.23= 2.81 Subtract exponents: (2)-(-5)=7 Answer: 2.81 X 107