Multiplying and Dividing in Scientific Notation Multiplying Numbers

Multiplying and Dividing in Scientific Notation

Multiplying Numbers in Scientific Notation • Multiply the coefficients together. • Add the exponents to get the power of 10. • General formula: (N X 10 x) (M X 10 y) = (N) (M) X 10 x+y

Example 1 • Given: (3. 42 X 105 )(4. 67 X 109) • Multiply coefficients: 3. 42 X 4. 67 = 15. 97 • Add Exponents: 105 x 109=105+9=1014 • Preliminary Answer (not in SN): 15. 97 X 1014 • Now, Rewrite in Scientific Notation if needed. • Final Answer: 1. 597 X 1015

Example 2 • Given: (2. 93 X 10 -2) (8. 3 X 10 -5) • Multiply Coefficients: 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 coefficients. • Then subtract the exponents • General formula:

Example 1 • Given: 8 • 10 -3 2 • 10 -2 • Divide coefficients: 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 coefficients: 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!! 3. Enter the exponent number. Use the +/- button to change its sign. Voila! To check yourself: multiply 6. 0 x 10 5 times 4. 0 x 103 on your calculator. Your answer should be 2. 4 x 109.

Practice Quiz 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 = ?