Algebra Section 8 Day 2: Scientific Notation Algebra: S8 Day 21

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation. Algebra: S8 Day 22

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer Algebra: S8 Day 23

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 Algebra: S8 Day 24

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 Algebra: S8 Day 25

Example 1: Express 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 x Algebra: S8 Day 26

Example 2: Write in scientific notation x x x x 10 5 Algebra: S8 Day 27

Example 3: Express 1.8 x in decimal notation Example 4: Express 4.58 x 10 6 in decimal notation. 4,580,000 Algebra: S8 Day 28

Write in PROPER scientific notation. (Notice the number is not between 1 and 10) x x x x 10 2 You may notice that when the decimal needs to be moved to the left you add to the exponent and when it is moved to the right, you subtract. Algebra: S8 Day 29

Example 5: Write x 10 5 in scientific notation x x x x x x x 10 8 Algebra: S8 Day 210

Operations with Scientific Notation To multiply two numbers in scientific notation you must multiply the base numbers and add the exponents on the base 10. To divide two numbers in scientific notation you must divide the base numbers and subtract the exponents on the base 10. Algebra: S8 Day 211

Example 6: 7.2 x x 10 2 Algebra: S8 Day 212

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Example 8: Write (2.8 x 10 3 )(5.1 x ) in scientific notation x x x x Algebra: S8 Day 214

Operations with Scientific Notation What about addition and subtraction?? You MUST convert the numbers to the same base 10 notation before adding or subtracting. After completing the addition/ subtraction problem you can switch the result back to proper scientific notation. Algebra: S8 Day 215

Example 9: Solve (3.7 x 10 3 )+(8.9 x 10 7 ) in scientific notation. Algebra: S8 Day 216

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Operations with Scientific Notation  Raising a Scientific Number to a Power First Raise the “Number” part to the exponent Then Multiply the power of the base 10 and the exponent together Algebra: S8 Day 218

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Homework Assignment 8-2 Algebra: S8 Day 220