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In which set are the numbers arranged in ascending order? (1 point)

3.25 × 10 , , , −3 2.25 × 10−3 3.25 × 10−4 1.25 × 10−3
0.00125, 0.00225, 0.000325, 0.00325
0.000325, 0.00225, 0.00125, 0.00325
3.25 × 10 , , , −4 1.25 × 10−3 2.25 × 10−3 3.25 × 10−3

3 answers

Let's convert all the given numbers into decimal form for clarity and then arrange them in ascending order.

  1. Scientific Notation Conversions:

    • \(3.25 \times 10^{-3} = 0.00325\)
    • \(2.25 \times 10^{-3} = 0.00225\)
    • \(3.25 \times 10^{-4} = 0.000325\)
    • \(1.25 \times 10^{-3} = 0.00125\)

  2. Decimal Values:

    • \(0.000325\)
    • \(0.00125\)
    • \(0.00225\)
    • \(0.00325\)

  3. Ascending Order: The numbers in ascending order are:

    • \(0.000325\)
    • \(0.00125\)
    • \(0.00225\)
    • \(0.00325\)

From the options provided, the set that shows these numbers in ascending order is: 0.000325, 0.00125, 0.00225, 0.00325.

which is right out of the 4

Let's analyze the provided options again based on the converted decimal values to determine which one is correct:

  1. Given Sets:

    • Set 1: \(3.25 \times 10^{-3}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-4}\)
    • Set 2: \(0.00125, 0.00225, 0.000325, 0.00325\)
    • Set 3: \(0.000325, 0.00225, 0.00125, 0.00325\)
    • Set 4: \(3.25 \times 10^{-4}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-3}\)

  2. Converted Values for Each Set:

    • Set 1:

      • \(3.25 \times 10^{-3} = 0.00325\)
      • \(1.25 \times 10^{-3} = 0.00125\)
      • \(2.25 \times 10^{-3} = 0.00225\)
      • \(3.25 \times 10^{-4} = 0.000325\)

    • Order: \(0.000325, 0.00125, 0.00225, 0.00325\) (not ascending)

    • Set 2:

      • \(0.00125, 0.00225, 0.000325, 0.00325\)

    • Order: Not ascending

    • Set 3:

      • \(0.000325, 0.00225, 0.00125, 0.00325\)

    • Order: Not ascending

    • Set 4:

      • \(3.25 \times 10^{-4} = 0.000325\)
      • \(1.25 \times 10^{-3} = 0.00125\)
      • \(2.25 \times 10^{-3} = 0.00225\)
      • \(3.25 \times 10^{-3} = 0.00325\)

    • Order: \(0.000325, 0.00125, 0.00225, 0.00325\) (correctly ascending)

From the analysis, Set 4 is the one that correctly puts all the numbers in ascending order:

3.25 × 10−4, 1.25 × 10−3, 2.25 × 10−3, 3.25 × 10−3.