Scientific Notation with positive powers of 10 Lesson 2.2 Mrs. Carley

Definition of Scientific Notation Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10 and a power of 10.

A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 9 and n is an integer

Example I Write 4,776 in scientific notation Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between one and ten. 4.776 Count the number of digits between the old and the new decimal point, this gives the power, n of 10 (10n). 4 776 3 Digits X 103 Since the decimal is shifted to the left, the exponent is positive. 4.776 x 103

Writing a number in Standard Notation Example #2 Video

Write the decimal number. Example #2 Write 4.953 x 104 in standard form Write the decimal number. 4.953 Move the decimal the number of places specified by the powers of ten: to the right since it is positive. 4 9530 X 104 4 Places Rewrite the number in integer/standard form. 49,530

Scientific notation with Negative Powers of 10 Lesson 2.3 Mrs. Carley

RULES Writing numbers in Scientific Notation When I move the decimal to the 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

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 Step 2: Count the number of places you moved the decimal point. Step 3: Any time you move the decimal point to the right….the exponent to the power of 10 is negative.

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. 2.87509 x 10-5 2.87509 x 10-4 2.87509 x 104 2.87509 x 105

Write 531.42 x 105 in scientific notation.

Writing a Number in Standard Notation Example #2

Example #2 Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10-6 in standard notation. Step1: Use the exponent to the power of 10 to see how many places to move the decimal point. 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 zeros if necessary. Answer: 0.00000233

Write the decimal number. Another Example Write 8.397 x 10-1 in standard form Write the decimal number. 8.397 Move the decimal the number of places specified by the powers of ten: to the left since it is negative. 0 8 397 X 10-1 1 Place Rewrite the number in integer/standard form. 0.8397

Express 1.8 x 10-4 in decimal notation. 0.00018 Express 4.58 x 106 in decimal notation. 4,580,000

Operations with Scientific Notation Lesson 2.4 Mrs. Carley

Adding/Subtracting Numbers Look at Example#1: Step1: Write each number in standard notation Step2: Complete the operation – add/ subtract Step3: Write the answer in scientific notation Complete #1 “Your Turn” on page 52.

Multiplying Numbers in Scientific Notation Multiply: (5.1 * 104) x (2.3 * 106) Multiply the coefficients: 5.1 * 2.3 = 11.73 Add the powers of 10: 4+6 =10 Check to be sure the product is in scientific notation. (5.1 * 104) x (2.3 * 106) = 11.73 * 1010 1.173 * 1011 Therefore, (5.1 * 104) x (2.3 * 106) = 1.173 * 1011

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

Dividing Numbers in Scientific Notation Divide (3.9 * 108) (6.5 * 10-4) Divide the coefficients: 3.9 / 6.5 = 0.6 Subtract the powers of 10: 8 – (-4) = 12 Check to be sure the quotient is in scientific notation. (3.9 * 108) = 0.6 * 1012) 6.0 * 1011

Example #2 Page 52 Complete #2-3 “your Turn”