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Which set of numbers is arranged in descending order?

1. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power
2. 7 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power
3. 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power
4. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7 x 10 to the negative thirty power

1 answer

To determine which set of numbers is arranged in descending order, we must compare each number based on its scientific notation.

  1. 7.6 x 10^(-25)
  2. 7.2 x 10^(-25)
  3. 7.2 x 10^(-30)
  4. 7 x 10^(-30)

To compare these effectively, we can rearrange them in terms of their exponent's value as well:

Numbers with larger negative exponents will be smaller than numbers with smaller negative exponents.

In this case:

  • \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\) are larger than \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\) since -25 is larger than -30.
  • Between \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\), \(7.6 x 10^{-25}\) is larger.
  • Among \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\), \(7.2 x 10^{-30}\) is larger.

Now, let's list all four numbers in descending order:

  1. \(7.6 x 10^{-25}\)
  2. \(7.2 x 10^{-25}\)
  3. \(7.2 x 10^{-30}\)
  4. \(7 x 10^{-30}\)

Now we can analyze the provided options:

  1. \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\) (Correct order)
  2. \(7 x 10^{-30}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7.6 x 10^{-25}\) (Incorrect order)
  3. \(7.2 x 10^{-30}, 7 x 10^{-30}, 7.6 x 10^{-25}, 7.2 x 10^{-25}\) (Incorrect order)
  4. \(7.6 x 10^{-25}, 7.2 x 10^{-30}, 7.2 x 10^{-25}, 7 x 10^{-30}\) (Incorrect order)

Therefore, the correct option representing numbers arranged in descending order is Option 1: \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\).