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Scientific Notation

Learn how to write large numbers using scientific notation, convert to standard form, and practice problems with detailed solutions.

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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. What do you do if the number is less than 1? • 0.000036 • 3.6 x 10 -5 • 0.0000007589 • 7.589 x 10 -7 • 0.000000000000256987 • 2.56987 x 10 -13 The decimal moves to the right And the exponent will be negative.

  12. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right if exponent is positive. • 3.4 x 105 in scientific notation • 340,000 in standard form

  13. 6.27 x 106 9.01 x 104 6,270,000 90,100 Write in Standard Form Move the decimal to the right.

  14. Scientific Notation to Standard Form • Move the decimal to the left is the exponent is negative. • 3.6 x 10-6 • 7.85 x 10-2

  15. 6.27 x 10 -6 9.01 x 10 -4 Write in Standard Form Move the decimal to the right.

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