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 7.2 × 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

Answer 1

To arrange the numbers in descending order, we need to compare their values, taking into account both the coefficients and the powers of 10.

The given numbers are:

1. \(7.6 \times 10^{-25}\)
2. \(7.2 \times 10^{-25}\)
3. \(7.2 \times 10^{-30}\)
4. \(7.0 \times 10^{-30}\)

To compare them, it's helpful to note the following:

• The larger the exponent (the power of 10), the larger the overall value (in the case of negative exponents, smaller absolute values become larger as you increase the exponent toward zero).
• Among numbers with the same exponent, the one with the larger coefficient is larger.

Now, we can compare:

• \(7.6 \times 10^{-25}\) and \(7.2 \times 10^{-25}\): \(7.6\) is greater than \(7.2\).
• \(7.2 \times 10^{-30}\) and \(7.0 \times 10^{-30}\): \(7.2\) is greater than \(7.0\).
• However, \(10^{-25}\) is greater than \(10^{-30}\) in terms of value.

So the numbers in descending order will be:

1. \(7.6 \times 10^{-25}\)
2. \(7.2 \times 10^{-25}\)
3. \(7.2 \times 10^{-30}\)
4. \(7.0 \times 10^{-30}\)

Thus, the set arranged in descending order is: \(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\).