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Scientific Notation

Scientific Notation. A short-hand way of writing large numbers without writing all of the zeros . The Distance From the Sun to the Earth. 93,000,000. Step 1. Move decimal left Leave only one number in front of decimal. 93,000,000 = 9.3000000. Step 2. Write number without zeros.

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Scientific Notation

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  1. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

  2. The Distance From the Sun to the Earth 93,000,000

  3. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

  4. Step 2 • Write number without zeros 93,000,000 = 9.3

  5. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  6. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

  7. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

  8. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

  9. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

  10. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

  11. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

  12. 6.27 x 106 9.01 x 104 6,270,000 90,100 Write in Standard Form Move the decimal to the right.

  13. Positive Exponents • 101 = 10 • 102 = 10X10= 100 • 103 = 10X10X10 = 1000 • 104 = 10X10X10X10 = 10,000

  14. Negative Exponents • 10-1 = 1/10 = 0.1 • 10-2 = 1/100 = 0.01 • 10-3 = 1/1000 = 0.001 • 10-4 = 1/10000 = 0.0001

  15. Scientific Notation • We use the idea of exponents to make it easier to work with large and small numbers. • 10,000 = 1 X 104 • 250,000 = 2.5 X 105 • Count places to the left until there is one number to the left of the decimal point. • 230,000 = ? • 35,000 = ?

  16. Scientific Notation Continued • 0.00006 = 6 X 10-5 • 0.00045 = 4.5 X 10-4 • Count places to the right until there is one number to the left of the decimal point • 0.003 = ? • 0.0000025 = ?

  17. Multiplying with Scientific Notation • Add the Exponents • 102 X 103 = 105 • 100 X 1000 = 100,000

  18. Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) • 230 X 3300 • Multiply the Coefficients • 2.3 X 3.3 = 7.59 • Add the Exponents • 102 X 103 = 105 • 7.59 X 105 • 759,000

  19. Multiplying with Scientific Notation • (4.6 X 104) X (5.5 X 103) = ? • (3.1 X 103) X (4.2 X 105) = ?

  20. Dividing with Scientific Notation • Subtract the Exponents • 104/103 = 101 • 10000X 1000 = 10

  21. Dividing with Scientific Notation • (3.3 X 104)/ (2.3 X 102) • 33000 / 230 = 143.4783 • Divide the Coefficients • 3.3/ 2.3 = 1.434783 • Subtract the Exponents • 104 / 102 = 102 • 1.4347823 X 102 • 143.4783

  22. Dividing with Scientific Notation • (4.6 X 104) / (5.5 X 103) = ? • (3.1 X 103) / (4.2 X 105) = ?

  23. Addition and subtraction Scientific Notation 2.0 x 102 + 3.0 x 103 .2 x 103 + 3.0 x 103 = .2+3 x 103 = 3.2 x 103 1. Make exponents of 10 the same 2. Add 0.2 + 3 and keep the 103 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x 107 - 6.3 x 105 2.0 x 107 -.063 x 107 = 2.0-.063 x 107 = 1.937 x 107 1. Make exponents of 10 the same 2. Subtract 2.0 - .063 and keep the 107 intact

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