Scientific Notation with Negative Powers of 10 2.3

Page 45 with a partner

Rules Writing numbers in Scientific Notation When I move the decimal to right, the exponent is negative When I move the decimal to the left the exponent is positive Writing numbers in Standard Notation When I move the decimal to the right, the number is larger When I move the decimal to the left, the number is smaller HINT: Think about the number line

Writing numbers in scientific notation

Example 1 The average size of an atom is about 0.00000003 centimeters across. Write the average size of an atom in scientific notation Step 1: Place the decimal point 3.0 Step 2: Count the number of places you moved the decimal point 8 Step 3: Any time you move the decimal point to the right…. The exponent to the power of 10 is negative 3.0 x 10-8

Express 0.0000000902 in scientific notation Where would the decimal go to make the number 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. 2.87509 x 10-4 3. 2.87509 x 104 4. 2.87509 x 105

Write 53,142,000 in scientific notation 1. 0.53142 x 102 2. 5.3142 x 103 3. 53.142 x 104 4. 531.42 x 105 5. 53.142 x 106 6. 5.3142x 107 7. 0.53142 x 10-7

Practice Page 46 #4-6

Writing numbers in standard notation

Example 2: Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10-6 meter. Write 2.33 x 10-6 in standard notation. Step 1: Use the exponent to the power of 10 to see how many places you need to move the decimal point 6 places Step 2: Place the decimal point. Since you are going to write a number less than 2.33, move the decimal point to the left. Add place holder zeroes if necessary. 0.00000233

Another Example: Write 8.397 x 10-1 in standard form Write the decimal number 8.397 Move the decimal point the number of places specified by the powers of ten: to the left since it is negative x 10-1 1 place 0.8.397 Rewrite the number in integer/standard form 0.8397

Examples Express 1.8 x 10-4 in decimal notation 0.00018 Expression 4.8 x 106 in decimal notation 4,800,000

Practice Pg 47 #7-11