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2.1 Scientific Notation SWBAT write very large or very small numbers in standard form in scientific notation, and vice versa SWBAT compare and order numbers in scientific notation Complete the Following Table From the Previous Table… • What patterns do you notice in the table? • How can you tell how many zeros are in a number based on the power of 10? Does anyone remember how to write a number in SCIENTIFIC NOTATION based on your science class or 6th grade math class? Writing a Number in Scientific Notation • Express one factor as a number greater than or equal to 1 but less than 10. Move the decimal point to the left or the right • Express the other factor as a power of 10. Count the number of places the decimal point was moved to the left or the right in the first factor, and use this number as the exponent on the power of ten Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where a is between 1 and 10 and n is an integer Think about it… • Let’s use the number 4,355 • How can I make this number bigger than zero, but less than 10? • Where would you place your decimal? • Why did you choose that position? So, what is the NEW number? 4.355 Continue… 4.355 • How many spaces did you move the decimal? • So let’s write this using Scientific Notation a x 10n “a” is the new number 10n , n is the number of spaces the decimal moved. 4.355 x 103 Write 28750.9 in scientific notation. 1. 2. 3. 4. 2.87509 x 10-5 2.87509 x 10-4 2.87509 x 104 2.87509 x 105 Scientific Notation Examples • Determine whether each of the following numbers is written in scientific notation? Explain. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 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 2.10,000,000,000,000,000,000,000. 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 Scientific Notation • Write each number in scientific notation. • 4) 62,400 • 5) 0.00085 • 6) 1,602,000 How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in standard notation. When numbers get this large, it is easier to write them in scientific notation. 2) Express 1.8 x 10-4 in standard notation. 0.00018 3) Express 4.58 x 106 in standard notation. 4,580,000 Write in Standard Form Comparing Scientific Notation • 1st compare the exponents of the powers of 10. The number with the greater exponent is the greater number • 2nd if the exponents are the same compare the decimal factors Compare Numbers 1. 4.078 × 10³ 2. 18.09 × 10⁴ 3. 7.154 × 10³ 4. 175 × 10³ 189.93 × 10² 70.188 × 10³ Order from least to greatest 4. 8.14 × 10², 9.03 × 10⁴, 81.4 × 10² 5. 7.375× 10¯², 7.45 ×10¯³, 8.1× 10¯⁴ What does Scientific Notation look like on a calculator? • Enter any 8-digit number into your calculator. • Next, multiply by a 4-digit number. • What do you see? Compare. Write <, =, or > Order from least to greatest Order from greatest to least