SCIENTIFIC NOTATION WITH NEGATIVE EXPONENTS 2 3 PAGE

SCIENTIFIC NOTATION WITH NEGATIVE EXPONENTS 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 positive – When I move the decimal to the left, the number is negative – 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. 000000902 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? • 7 • When the original number is less than 1, the exponent is negative • 9. 02 x 10 -7

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

WRITE 531. 42 X 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. 3142 x 107 • 7. 0. 53142 x 10 -7 5 10 IN SCIENTIFIC

PRACTICE • Page 46 #4 -7

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: -1 WRITE 8. 397 X 10 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. 58 x 106 in decimal notation • 4, 580, 000

PRACTICE • Pg 47 #7 -11