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Scientific Notation

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Scientific Notation

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Scientific Notation

  1. 1. ScientificNotationPowers of 10
  2. 2. Warm UpEvaluate each expression.1. 123 1,000 123,0002. 123 1,000 0.1233. 0.003 100 0.34. 0.003 100 0.000035. 104 10,0006. 10–4 0.00017. 230 1
  3. 3. ObjectivesEvaluate and multiply by powers of 10.Convert between standard notation andscientific notation.
  4. 4. The table shows relationships between several powers of 10.Each time you divide by 10, the exponent decreases by 1 and the decimal pointmoves one place to the left.
  5. 5. The table shows relationships between several powers of 10.Each time you multiply by 10, the exponent increases by 1 and the decimalpoint moves one place to the right.
  6. 6. Example 1: Evaluating Powers of 10Find 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
  7. 7. Writing MathYou may need to add zeros to the right or left of anumber in order to move the decimal point in thatdirection.
  8. 8. Check It Out! Example 1 Find the value of each power of 10.a. 10–2 b. 105 c. 1010Start with 1 and Start with 1 and Start with 1 andmove the decimal move the decimal move the decimalpoint two places to point five places to point ten places tothe left. the right. the right. 0.01 100,000 10,000,000,000
  9. 9. Reading MathIf you do not see a decimal point in a number, it isunderstood to be at the end of the number.
  10. 10. Example 2: Writing Powers of 10Write 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.
  11. 11. Check It Out! Example 2 Write each number as a power of 10.a. 100,000,000 b. 0.0001 c. 0.1The decimal point is The decimal point The decimal pointeight places to the is four places to the is one place to theright of 1, so the left of 1, so the left of 1, so theexponent is 8. exponent is –4. exponent is –1.
  12. 12. You can also move the decimal point to find the value ofany number multiplied by a power of 10. You start with thenumber rather than starting with 1. Multiplying by Powers of 10
  13. 13. Example 3: Multiplying by Powers of 10Find 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
  14. 14. Check It Out! Example 3Find 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
  15. 15. Scientific notation is a method of writing numbers that arevery large or very small. A number written in scientificnotation 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.
  16. 16. Example 4A: Astronomy ApplicationSaturn has a diameter of about km. Its distancefrom 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
  17. 17. Example 4B: Astronomy ApplicationSaturn has a diameter of about km. Its distancefrom the Sun is about 1,427,000,000 km.Write Saturn’s distance from the Sun in scientificnotation. 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.
  18. 18. Reading MathStandard form refers to the usual way that numbers arewritten—not in scientific notation.
  19. 19. Check It Out! Example 4aUse the information above to write Jupiter’s diameter inscientific 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
  20. 20. Check It Out! Example 4bUse the information above to write Jupiter’s orbital speedin standard form. 13000 Move the decimal point 4 places to the right. 13,000 m/s
  21. 21. Example 5: Comparing and Ordering Numbers in Scientific NotationOrder 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
  22. 22. Check It Out! Example 5Order 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
  23. 23. Lesson Quiz: Part IFind the value of each expression.1. 3,745,0002. 0.002933. 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
  24. 24. Lesson Quiz: Part IIFind the value of each expression. 4. Order the list of numbers from least to greatest

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