Warm Up a) Order each set of numbers from least to greatest 104 , 10-2, 100, 10-1 10-2 10-1 100 104 82 , 8-2, 83, 80 8-2 80 82 83 23 , 2-6, 2-4, 21 2-6 2-4 21 23 Order the powers from least to greatest (10-4)5, (10-3)7, (10-8)-2. b) 10-20 10-21 1016 2 1 3

Lesson 3-3 Scientific Notation You'll Learn how to Express large and small numbers in scientific Notation Compare two numbers written in scientific Notation

Express large and small numbers in scientific Notation An abbreviation or shorthand way of writing very large or very small numbers. Distance from earth to the closest start outside our solar system 25,300,000,000,000 Kilometers Number of atoms in a glass of water 30,600,000,000,000,000,000,000,000 atoms Weight of a proton 0.000 000 000 000 000 000 368 grams

Write each number in scientific notation Convert from standard form to scientific notation. EXAMPLE 1 Write each number in scientific notation . . Move the decimal point and count the number of spots, until there is exactly one digit to the left of the decimal point. 1) 25300000000000 ₓ = 2.53 1013 Place the Decimal point in the new position and get rid of all the zeros Count the number of spots . . 2) 0 000000000000000000368 ₓ = 3.68 10-19 The sign of the exponent Left (+) Right (–)

Write each number in scientific notation Your Turn ₓ 1) 600000000000000000 = 6 1017 ₓ 2) 0.000000000012 = 1.2 10-11 ₓ 3) 0.00709 = 7.09 10-3

Therefore 1st cell has a greater diameter Science application A certain cell has a diameter of approximately 4.11 ˣ 10-5 meters. A second cell has a diameter of 1.5 ˣ 10-5. which cell has a greater diameter EXAMPLE 3 4.11 ₓ 10-5 1st cell Compare the powers of 10 1.5 ₓ 10-5 2nd cell Compare the numbers Therefore 1st cell has a greater diameter

Write each number in Standard notation Convert from scientific notation to standard form EXAMPLE 2 Write each number in Standard notation 1) 1.35 ₓ 108 Move the decimal point 8 places to the right then add in zeros in the empty spots = 1 35 . = 135 2) 2.7 ₓ 10-4 Move the decimal point 4 places to the left then add in zeros in the empty spots = . 2 7 . = . 2 7

Write each number in standard notation Your Turn 1) 2.01 ₓ 107 = 20100000 2) 3.04 ₓ 10-3 = 0.00304

Lesson Quiz: Part I Write each number in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write each number in scientific notation. 5.3  10–3 3. 0.0053 5.7  107 4. 57,000,000 5. Order the numbers from least to greatest. T 2  10–4, 9  10–5, 7  10–5 7  10–5, 9  10–5, 2  10–4

Lesson Quiz: Part II 6. A human body contains about 5.6  106 microliters of blood. Write this number in standard notation. 5,600,000

Lesson Quiz for Student Response Systems 1. Write the number in standard notation. 3.2  103 A. 32 B. 320 C. 3200 D. 32000 11

Lesson Quiz for Student Response Systems 2. Write the number in scientific notation. 0.0978 A. 0.978  10–1 B. 9.78  10–1 C. 9.78  10–2 D. 9.78  10–3 12

Lesson Quiz for Student Response Systems 3. Write the number in scientific notation. 13,432 A. 1.3432  104 B. 13.432  10–4 C. 1.3432  10–4 D. 13.432  104 13