Scientific Notation Notes Physical Science Freshman Physics Objective

Scientific Notation Notes Physical Science (Freshman Physics)

Objective The student will be able to: express numbers in scientific and decimal notation.

How wide is our universe? 210, 000, 000, 000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 (there can be only 1 number in front of the decimal) and n is an integer

Write the width of the universe in scientific notation. 210, 000, 000, 000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2. 10, 000, 000, 000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2. 1 x 1023

1) Express 0. 0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9. 02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9. 02 x 10 -8

Write 28750. 9 in scientific notation. 1. 2. 87509 x 10 -5 2. 87509 x 10 -4 3. 2. 87509 x 104 4. 2. 87509 x 105

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

6 10 IF the exponents are the 4 x 6 + ________ 3 x 10 same, we simply add or subtract the numbers in 6 7 x 10 front and bring the exponent down unchanged.

4 + 3 x x 106 If the exponents are 105 NOT the same, we must move a decimal to make them the same.

Determine which of the numbers has the smaller exponent. 1. Change this number by moving the decimal place to the left and raising the exponent, until the exponents of both numbers agree. Note that this will take the lesser number out of standard form. 2. Add or subtract the coefficients as needed to get the new coefficient. 3. The exponent will be the exponent that both numbers share. 4. Put the number in standard form.

6 10 4. 00 x 6 5 +. 30 x 10 + 3. 00 x 10 Move the decimal on the smaller number to the left and raise the exponent ! Note: This will take the lesser number out of standard form.

4. 00 + 3. 00 6 10 x 4. 00 x 6 5 x 10 +. 30 x 10 6 4. 30 x 10 Add or subtract the coefficients as needed to get the new coefficient. The exponent will be the exponent that both numbers share.

Make sure your final answer is in scientific notation. If it is not, convert it to scientific notation.

A Problem for you… -6 10 2. 37 x -4 + 3. 48 x 10

Solution… -6 002. 37 x 10 -4 + 3. 48 x 10

Solution… 0. 0237 + 3. 48 3. 5037 -4 10 x -4 x 10

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLYING AND DIVIDING

Rule for Multiplication When multiplying with scientific notation: 1. Multiply the coefficients together. 2. Add the exponents. 3. The base will remain 10.

(2 x 103) • (3 x 105) = 6 x 108

(4. 6 x 108) (5. 8 x 106) =26. 68 x 1014 Notice: What is wrong with this example? Although the answer is correct, the number is not in scientific notation. To finish the problem, move the decimal one space left and increase the exponent by one. 26. 68 x 1014 = 2. 668 x 1015

((9. 2 x 105) x (2. 3 x 107) = 21. 16 x 1012 = 2. 116 x 1013

(3. 2 x 10 -5) x (1. 5 x 10 -3) = 4. 8 • 10 -8

Rule for Division When dividing with scientific notation 1. Divide the coefficients 2. Subtract the exponents. 3. The base will remain 10.

(8 • 106) ÷ (2 • 103) = 4 x 103

Please multiply the following numbers. (5. 76 x 102) x (4. 55 x 10 -4) = (3 x 105) x (7 x 104) = (5. 63 x 108) x (2 x 100) = (4. 55 x 10 -14) x (3. 77 x 1011) = (8. 2 x 10 -6) x (9. 4 x 10 -3) =

Please multiply the following numbers. (5. 76 x 102) x (4. 55 x 10 -4) = (3 x 105) x (7 x 104) = (5. 63 x 108) x (2 x 100) = (4. 55 x 10 -14) x (3. 77 x 1011) = (8. 2 x 10 -6) x (9. 4 x 10 -3) = 2. 62 x 10 -1 2. 1 x 1010 1. 13 x 109 1. 72 x 10 -2 7. 71 x 10 -8

Please divide the following numbers. 1. (5. 76 x 102) / (4. 55 x 10 -4) = 2. (3 x 105) / (7 x 104) = 3. (5. 63 x 108) / (2) = 4. (8. 2 x 10 -6) / (9. 4 x 10 -3) = 5. (4. 55 x 10 -14) / (3. 77 x 1011) =

Please divide the following numbers. 1. (5. 76 x 102) / (4. 55 x 10 -4) = 1. 27 x 106 2. (3 x 105) / (7 x 104) = 4. 3 x 100 = 4. 3 3. (5. 63 x 108) / (2 x 100) = 2. 82 x 108 4. (8. 2 x 10 -6) / (9. 4 x 10 -3) = 8. 7 x 10 -4 5. (4. 55 x 10 -14) / (3. 77 x 1011) = 1. 2 x 10 -25

9. 54 x 107 miles 1. 86 x 107 miles per second Scientific Notation Makes These Numbers Easy