Compare Very Large and Very Small Numbers Quick Check

Question

4 of 54 of 5 Items
Question
Which set of numbers is arranged in descending order?(1 point)
Responses

7.6 × 10−25
, 7.2 × 10−25
, 7.2 × 10−30
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline

7.6 × 10−25
, 7.2 × 10−30
, 7.2 × 10−25
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7 times 10 Superscript negative 30 Baseline

7 × 10−30
, 7.2 × 10−25
, 7.2 × 10−30
, 7.6 × 10−25
7 times 10 Superscript negative 30 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7.6 times 10 Superscript negative 25 Baseline

7.2 × 10−30
, 7 × 10−30
, 7.6 × 10−25
, 7.2 × 10−25
7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline , 7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline
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Answer 1

To determine which set of numbers is arranged in descending order, we need to compare their values based on the scientific notation.

The given numbers are:

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

Now, let's understand the order of magnitude of these numbers:

• Both \(7.6 \times 10^{-25}\) and \(7.2 \times 10^{-25}\) are in the same order of magnitude \(10^{-25}\), and \(7.6\) is greater than \(7.2\).

• \(7.2 \times 10^{-30}\) and \(7 \times 10^{-30}\) are in the order of magnitude \(10^{-30}\). Here, \(7.2\) is greater than \(7\).

When comparing \(10^{-25}\) and \(10^{-30}\), \(10^{-25}\) is larger than \(10^{-30}\). Thus, we can say:

• \(7.6 \times 10^{-25}\) > \(7.2 \times 10^{-25}\) > \(7.2 \times 10^{-30}\) > \(7 \times 10^{-30}\)

With this in mind, the correct order from largest to smallest is:

• \(7.6 \times 10^{-25}\)
• \(7.2 \times 10^{-25}\)
• \(7.2 \times 10^{-30}\)
• \(7 \times 10^{-30}\)

Thus, the correct response representing this descending order is: \(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\).