1. PRE-ALGEBRA

2. Lesson 4-9 Warm-Up

3. PRE-ALGEBRA “Scientific Notation” (4-9) What is “scientific notation”? How do you write a number in scientific notation? scientific notation: a way to write very large numbers in short form using powers of 10 in the form a x 10 n, where n is an integer and a is between 1 and 10 (1 ≤ a ≤ 10). Example: 7,500,000,000,000 (“7 trillion, 500 billion”) = 7.5 x 10 12 To write a number in scientific notation, move the decimal so it’s after the first nonzero (≠ 0) digit, write the rest of the nonzero numbers after the decimal, and multiply this by 10 to the power of the number of jumps it would take to make the original number (right jumps = positive exponent and left jumps = negative exponent). Standard Notation: the usual way to write a number using commas, etc. Examples: The world’s largest tree is the General Sherman at, 2,777,000 pounds.Write this weight in scientific notation. Move the decimal point to get a number greater than 1 but less than 10. Drop the zeros after the last nonzero digit Since you moved the decimal 6 places to the left to make a smaller number, make the exponent a positive 6 __._____ x 10 ___  decimal jumps it would take to make the number  first rest of nonzero the nonzero digit digits

4. PRE-ALGEBRA “Scientific Notation” (4-9) What is “standard notation”? How do you change scientific notation to standard notation? Examples: Write 0.000079 in scientific notation. Move the decimal point to get a number greater than 1 but less than 10. Drop the zeros before the first nonzero digit Since you moved the decimal 5 places to the right to make a bigger number, make the exponent a negative 5 Standard Notation: the usual way to write a number using commas, etc. standard notation: the way you normally write numbers using place value To change scientific notation to standard notation, move the decimal the number of places the exponent tells you to. Move the decimal to the right for positive exponents (make a bigger number) and to the left for negative exponents (make number smaller). Scientific Notation Standard Notation 3.6 x 10 12 (3.6 trillion) 3,600,000,000,000 4.36 x 10 -11 0.0000000000436

5. PRE-ALGEBRA About 6,300,000 people visited the Eiffel Tower in the year 2000. Write this number in scientific notation. 6,300,000 6.3Drop the zeros after the 3. 6.3  10 6 You moved the decimal point 6 places. The original number is greater than 10.Use 6 as the exponent of 10. Move the decimal point to get a decimal greater than 1 but less than 10. 6 places Scientific Notation LESSON 4-9 Additional Examples

6. PRE-ALGEBRA Write 0.00037 in scientific notation. 0.00037Move the decimal point to get a decimal greater than 1 but less than 10. 4 places 3.7  10 –4 You moved the decimal point 4 places. The original number is less than 1.Use –4 as the exponent of 10. 3.7Drop the zeros before the 3. Scientific Notation LESSON 4-9 Additional Examples

7. PRE-ALGEBRA Write each number in standard notation. a. 3.6  10 4 3.6000Write zeros while moving the decimal point. 36,000Rewrite in standard notation. b. 7.2  10 –3 007.2 0.0072Rewrite in standard notation. Write zeros while moving the decimal point. Scientific Notation LESSON 4-9 Additional Examples

8. PRE-ALGEBRA Write each number in scientific notation. a. 0.107  10 12 0.107  10 12 = 1.07  10 –1  10 12 Write 0.107 as 1.07  10 –1. = 1.07  10 11 Add the exponents. b. 515.2  10 –4 515.2  10 –4 = 5.152  10 2  10 –4 Write 515.2 as 5.152  10 2. = 5.152  10 –2 Add the exponents. Scientific Notation LESSON 4-9 Additional Examples

9. PRE-ALGEBRA “Scientific Notation” (4-9) How do you order numbers in scientific notation? To order numbers in scientific notation, order by the exponents only first, If there is a tie with the exponents, order by the decimal next. Examples: Order 0.064 x 10 8, 312 x 10 -4, and 0.58 x 10 7 from least to greatest. Step 1: Write each number in correct scientific notation. Step 2: Order the powers of 10 from least to greatest first. Arrange the decimals with the same power of 10 from least to greatest if necessary. Step 3: Write the original numbers in order from least to greatest.

10. PRE-ALGEBRA Write each number in scientific notation. 0.035  10 4 0.69  10 2 3.5  10 2 710  10 –1 7.1  106.9  10 Order the powers of 10. Arrange the decimals with the same power of 10 in order. 6.9  10 1 7.1  10 1 3.5  10 2 Write the original numbers in order. 0.69  10 2, 710  10 –1, 0.035  10 4 Order 0.035  10 4, 710  10 –1, and 0.69  10 2 from least to greatest. Scientific Notation LESSON 4-9 Additional Examples

11. PRE-ALGEBRA “Scientific Notation” (4-9) How do multiply numbers in scientific notation? To multiply numbers in scientific notation, multiply the decimals and powers of 10 separately. Then, put the answer in correct scientific notation form. Examples: The Great Pyramid of Giza in Egypt contains about 2.3 x 10 6 blocks of stone. On average, each block weighs about 5 x 10 3 ponds. About how heavy is the Pyramid? (2.3 x 10 6 )(5 x 10 3 )Multiply the number of blocks by the weight of each block to find the total weight. = 2.3 x 5 x 10 6 x 10 3 Use the Commutative Property of Multiplication to rearrange the terms. = 11.5 x 10 6 x 10 3 Multiply the decimals. = 11.5 x 10 9 Add the exponents = (1.15 x 10 1 ) x 10 9 Write 11.5 x 10 9 in correct scientific notation = 1.15 x 10 10 Add the exponents The Great Pyramid of Giza weighs about 1.15 x 10 10 lb.

12. PRE-ALGEBRA Multiply 4  10 –6 and 7  10 9. Express the result in scientific notation. Use the Commutative Property of Multiplication. (4  10 –6 )(7  10 9 ) = 4  7  10 –6  10 9 = 28  10 –6  10 9 Multiply 4 and 7. = 28  10 3 Add the exponents. = 2.8  10 1  10 3 Write 28 as 2.8  10 1. = 2.8  10 4 Add the exponents. Scientific Notation LESSON 4-9 Additional Examples

13. PRE-ALGEBRA Scientists find a wooly mammoth fossil that is about 2.0  10 4 years old. They believe that Earth is about 2.3  10 5 times as old as this fossil. How old do they believe Earth is? (2.0  10 4 )(2.3  10 5 ) Multiply age of fossil by the number of times as old as this fossil Earth is. = 2.0  2.3  10 4  10 5 Use Commutative Property of Multiplication. = 4.6  10 4  10 5 Multiply 2.0 and 2.3. = 4.6  10 9 Add the exponents. Earth is about 4.6  10 9 years old. Scientific Notation LESSON 4-9 Additional Examples

14. PRE-ALGEBRA Write each number in scientific notation. 1.5,400,0002.0.0000867 Write each number in standard notation. 3.3.45  10 6 4.1.99  10 –5 5.Order 7.2  10 5, 7.2  10 6, 7.02  10 6, and 7.1  10 –6 from least to greatest. 6.Multiply 14  10 6 and 4  10 –4. Express the result in scientific notation. 5.6  10 3 5.4  10 6 8.67  10 –5 3,450,0000.0000199 7.1  10 –6, 7.2  10 5, 7.02  10 6, 7.2  10 6 Lesson Quiz Scientific Notation LESSON 4-9