ofof 1010 and Scientific Notation 7 2 Powers

ofof 1010 and Scientific Notation 7 -2 Powers Warm Up Lesson Presentation Lesson Quiz Holt Algebra 11

7 -2 Powers of 10 and Scientific Notation Warm Up Evaluate each expression. 1. 123 1, 000 123, 000 2. 123 1, 000 0. 123 3. 0. 003 100 0. 3 4. 0. 003 100 0. 00003 5. 104 10, 000 6. 10– 4 0. 0001 7. 230 1 Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Objectives Evaluate and multiply by powers of 10. Convert between standard notation and scientific notation. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Vocabulary scientific notation Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation The table shows relationships between several powers of 10. Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation The table shows relationships between several powers of 10. Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Example 1: Evaluating Powers of 10 Find the value of each power of 10. A. 10– 6 B. 104 C. 109 Start with 1 and move the decimal point six places to the left. 0. 000001 Start with 1 and move the decimal point four places to the right. 10, 000 Start with 1 and move the decimal point nine places to the right. 1, 000, 000 Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Writing Math You may need to add zeros to the right or left of a number in order to move the decimal point in that direction. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 1 Find the value of each power of 10. a. 10– 2 b. 105 c. 1010 Start with 1 and move the decimal point two places to the left. 0. 01 Start with 1 and move the decimal point five places to the right. 100, 000 Start with 1 and move the decimal point ten places to the right. 10, 000, 000 Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Reading Math If you do not see a decimal point in a number, it is understood to be at the end of the number. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Example 2: Writing Powers of 10 Write each number as a power of 10. A. 1, 000 B. 0. 0001 C. 1, 000 The decimal point is six places to the right of 1, so the exponent is 6. The decimal point is four places to the left of 1, so the exponent is – 4. The decimal point is three places to the right of 1, so the exponent is 3. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 2 Write each number as a power of 10. a. 100, 000 b. 0. 0001 c. 0. 1 The decimal point is eight places to the right of 1, so the exponent is 8. The decimal point is four places to the left of 1, so the exponent is – 4. The decimal point is one place to the left of 1, so the exponent is – 1. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1. Multiplying by Powers of 10 Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23. 89 108 23. 8 9 0 0 0 2, 389, 000 Move the decimal point 8 places to the right. B. 467 10– 3 467 0. 467 Holt Algebra 1 Move the decimal point 3 places to the left.

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 3 Find the value of each expression. a. 853. 4 105 853. 4 0 0 85, 340, 000 Move the decimal point 5 places to the right. b. 0. 163 10– 2 0. 0 0163 0. 00163 Holt Algebra 1 Move the decimal point 2 places to the left.

7 -2 Powers of 10 and Scientific Notation Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied. The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Example 4 A: Astronomy Application Saturn has a diameter of about Its distance from the Sun is about 1, 427, 000 km. Write Saturn’s diameter in standard form. 120000 120, 000 km Holt Algebra 1 Move the decimal point 5 places to the right.

7 -2 Powers of 10 and Scientific Notation Example 4 B: Astronomy Application Saturn has a diameter of about Its distance from the Sun is about 1, 427, 000 km. Write Saturn’s distance from the Sun in scientific notation. Count the number of places 1, 427, 000 you need to move the decimal point to get a 1, 4 2 7, 0 0 0 number between 1 and 10. 9 places 1. 427 109 km Holt Algebra 1 Use that number as the exponent of 10.

7 -2 Powers of 10 and Scientific Notation Reading Math Standard form refers to the usual way that numbers are written—not in scientific notation. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 4 a Use the information above to write Jupiter’s diameter in scientific notation. 143, 000 km 143000 5 places 1. 43 105 km Holt Algebra 1 Count the number of places you need to move the decimal point to get a number between 1 and 10. Use that number as the exponent of 10.

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 4 b Use the information above to write Jupiter’s orbital speed in standard form. 13000 13, 000 m/s Holt Algebra 1 Move the decimal point 4 places to the right.

7 -2 Powers of 10 and Scientific Notation Example 5: Comparing and Ordering Numbers in Scientific Notation Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Check It Out! Example 5 Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. 2 10 -12, 4 10 -3, 5. 2 10 -3, 3 1014, 4. 5 1030 Step 2 Order the numbers that have the same power of 10. Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Lesson Quiz: Part I Find the value of each expression. 1. 3, 745, 000 2. 0. 00293 3. The Pacific Ocean has an area of about 6. 4 х 107 square miles. Its volume is about 170, 000 cubic miles. a. Write the area of the Pacific Ocean in standard form. b. Write the volume of the Pacific Ocean in scientific notation. 1. 7 108 mi 3 Holt Algebra 1

7 -2 Powers of 10 and Scientific Notation Lesson Quiz: Part II Find the value of each expression. 4. Order the list of numbers from least to greatest Holt Algebra 1