1 / 23

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.

pallaton
Download Presentation

Scientific Notation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related