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Order the numbers from smallest to largest. Use the number line as a guide to ensure you put the numbers in the correct order.

1. 9.3 * 10^-7
2. -7.6 * 10^-9
3. 5.7 * 10^13
4. 3.2 * 10^4
5. 4.5 * 10^4
6. 1.9 * 10^7

1 answer

To order the numbers from smallest to largest, we first need to convert them into decimal notation for easier comparison:

  1. \( 9.3 \times 10^{-7} = 0.00000093 \)
  2. \( -7.6 \times 10^{-9} = -0.0000000076 \)
  3. \( 5.7 \times 10^{13} = 57000000000000 \)
  4. \( 3.2 \times 10^{4} = 32000 \)
  5. \( 4.5 \times 10^{4} = 45000 \)
  6. \( 1.9 \times 10^{7} = 19000000 \)

Now we can write them all out in decimal form:

  • \( -7.6 \times 10^{-9} = -0.0000000076 \)
  • \( 9.3 \times 10^{-7} = 0.00000093 \)
  • \( 3.2 \times 10^{4} = 32000 \)
  • \( 4.5 \times 10^{4} = 45000 \)
  • \( 1.9 \times 10^{7} = 19000000 \)
  • \( 5.7 \times 10^{13} = 57000000000000 \)

Now we can order these numbers from smallest to largest:

  1. \( -7.6 \times 10^{-9} \)
  2. \( 9.3 \times 10^{-7} \)
  3. \( 3.2 \times 10^{4} \)
  4. \( 4.5 \times 10^{4} \)
  5. \( 1.9 \times 10^{7} \)
  6. \( 5.7 \times 10^{13} \)

So the ordered list is:

  1. \( -7.6 \times 10^{-9} \)
  2. \( 9.3 \times 10^{-7} \)
  3. \( 3.2 \times 10^{4} \)
  4. \( 4.5 \times 10^{4} \)
  5. \( 1.9 \times 10^{7} \)
  6. \( 5.7 \times 10^{13} \)