Scientific Notation
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This document provides instruction on scientific notation and powers of 10. It begins with examples of evaluating and multiplying numbers by powers of 10 by moving the decimal point left or right. It then discusses writing numbers in terms of powers of 10 based on the number of places the decimal point is from 1. The document also covers converting between standard notation and scientific notation. It applies these concepts to astronomy examples of writing planet diameters and distances in standard and scientific notation. Finally, it discusses comparing and ordering numbers expressed in scientific notation.
Scientific Notation
- 2. 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
- 3. Objectives Evaluate and multiply by powers of 10. Convert between standard notation and scientific notation.
- 4. 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.
- 5. 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.
- 7. 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 Start with 1 and Start with 1 and move the decimal move the decimal move the decimal point six places to point four places to point nine places to the left. the right. the right. 0.000001 10,000 1,000,000,000
- 8. 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.
- 9. Check It Out! Example 1 Find the value of each power of 10. a. 10–2 b. 105 c. 1010 Start with 1 and Start with 1 and Start with 1 and move the decimal move the decimal move the decimal point two places to point five places to point ten places to the left. the right. the right. 0.01 100,000 10,000,000,000
- 10. Reading Math If you do not see a decimal point in a number, it is understood to be at the end of the number.
- 11. Example 2: Writing Powers of 10 Write each number as a power of 10. A. 1,000,000 B. 0.0001 C. 1,000 The decimal point is The decimal point The decimal point is six places to the right is four places to the three places to the of 1, so the exponent left of 1, so the right of 1, so the is 6. exponent is –4. exponent is 3.
- 12. Check It Out! Example 2 Write each number as a power of 10. a. 100,000,000 b. 0.0001 c. 0.1 The decimal point is The decimal point The decimal point eight places to the is four places to the is one place to the right of 1, so the left of 1, so the left of 1, so the exponent is 8. exponent is –4. exponent is –1.
- 13. 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
- 14. Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23.89 108 23.8 9 0 0 0 0 0 0 Move the decimal point 8 places to the right. 2,389,000,000 B. 467 10–3 467 Move the decimal point 3 places to the left. 0.467
- 15. Check It Out! Example 3 Find the value of each expression. a. 853.4 105 853.4 0 0 0 0 Move the decimal point 5 places to the right. 85,340,000 b. 0.163 10–2 0.0 0163 Move the decimal point 2 places to the left. 0.00163
- 16. 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.
- 17. Example 4A: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s diameter in standard form. 120000 Move the decimal point 5 places to the right. 120,000 km
- 18. Example 4B: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s distance from the Sun in scientific notation. 1,427,000,000 Count the number of places you need to move the 1,4 2 7,0 0 0,0 0 0 decimal point to get a number between 1 and 10. 9 places Use that number as the 1.427 109 km exponent of 10.
- 19. Reading Math Standard form refers to the usual way that numbers are written—not in scientific notation.
- 20. Check It Out! Example 4a Use the information above to write Jupiter’s diameter in scientific notation. 143,000 km Count the number of places you need to move the 143000 decimal point to get a number between 1 and 10. 5 places Use that number as the exponent of 10. 1.43 105 km
- 21. Check It Out! Example 4b Use the information above to write Jupiter’s orbital speed in standard form. 13000 Move the decimal point 4 places to the right. 13,000 m/s
- 22. 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
- 23. 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 1014, 4.5 1030 Step 2 Order the numbers that have the same power of 10
- 24. 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 170,000,000 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 mi3
- 25. Lesson Quiz: Part II Find the value of each expression. 4. Order the list of numbers from least to greatest