Which set of numbers is arranged in descending order?
A. 7.6 × 10^-²⁵, 7.2 × 10^-³⁰, 7.2 × 10^-²⁵, 7 × 10^-³⁰
B. 7 × 10^-³⁰, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7.6 × 10^-²⁵
C. 7.6 × 10^-²⁵, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7 × 10^-³⁰
D. 7.2 × 10^-³⁰, 7 × 10^-³⁰, 7.6 × 10^-²⁵, 7.2 × 10^-²⁵
The set of numbers arranged in descending order is:
B. 7 × 10^-³⁰, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7.6 × 10^-²⁵
In which set are the numbers arranged in ascending order?
A. 0.00125, 0.00225, 0.000325, 0.00325
B. 3.25 × 10^-³, 2.25 × 10^-³, 3.25 × 10^-⁴, 1.25 × 10^‐³
C. 3.25 × 10^-⁴, 1.25 × 10^-³, 2.25 × 10^-³, 3.25 × 10^-³
D. 0.000325, 0.00225, 0.00125, 0.00325
The set of numbers arranged in ascending order is:
D. 0.000325, 0.00225, 0.00125, 0.00325
To arrange the numbers in descending order, we compare the coefficient part (7.6, 7.2, 7.2, 7) and then the exponent part (-²⁵, -²⁵, -³⁰, -³⁰).
Comparing the coefficient part of the numbers, we start with the largest coefficient:
7.6 > 7.2 > 7.2 > 7.
Since the coefficient parts are equal for the 2nd and 3rd numbers, we move on to comparing the exponent part:
-²⁵ > -²⁵ > -³⁰ > -³⁰.
Now, let's combine the coefficient and exponent parts in descending order:
7.6 × 10^-²⁵, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7 × 10^-³⁰.
Therefore, the correct set of numbers arranged in descending order is option A.
To determine which set of numbers is arranged in descending order, you can compare the exponent values of the scientific notation.
Let's examine each option:
A. 7.6 × 10^-²⁵, 7.2 × 10^-³⁰, 7.2 × 10^-²⁵, 7 × 10^-³⁰
The first number has an exponent of -²⁵, while the second number has an exponent of -³⁰. The first number has a smaller exponent, so it should come after the second number in a descending order. Comparing the third and fourth numbers, they have the same exponent of -³⁰, but the third number (7.2 × 10^-²⁵) has a larger coefficient than the fourth number (7 × 10^-³⁰). This means that the fourth number should come before the third number in a descending order. Therefore, this set is not arranged in descending order.
B. 7 × 10^-³⁰, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7.6 × 10^-²⁵
The first number has an exponent of -³⁰, while the second number has an exponent of -²⁵. The second number has a larger exponent, so it should come before the first number in a descending order. Comparing the third and fourth numbers, they have the same exponent of -²⁵, but the fourth number (7.6 × 10^-²⁵) has a larger coefficient than the third number (7.2 × 10^-³⁰). This means that the fourth number should come before the third number in a descending order. Therefore, this set is arranged in descending order.
C. 7.6 × 10^-²⁵, 7.2 × 10^-²⁵, 7.2 × 10^-³⁰, 7 × 10^-³⁰
The first two numbers have the same exponent of -²⁵, but the first number (7.6 × 10^-²⁵) has a larger coefficient than the second number (7.2 × 10^-²⁵). This means that the first number should come before the second number in a descending order. Comparing the third and fourth numbers, they have the same exponent of -³⁰, but the third number (7.2 × 10^-³⁰) has a larger coefficient than the fourth number (7 × 10^-³⁰). This means that the third number should come before the fourth number in a descending order. Therefore, this set is not arranged in descending order.
D. 7.2 × 10^-³⁰, 7 × 10^-³⁰, 7.6 × 10^-²⁵, 7.2 × 10^-²⁵
The first two numbers have the same exponent of -³⁰, but the first number (7.2 × 10^-³⁰) has a larger coefficient than the second number (7 × 10^-³⁰). This means that the first number should come before the second number in a descending order. Comparing the third and fourth numbers, they have the same exponent of -²⁵, but the third number (7.6 × 10^-²⁵) has a larger coefficient than the fourth number (7.2 × 10^-²⁵). This means that the third number should come before the fourth number in a descending order. Therefore, this set is arranged in descending order.
Hence, the correct answer is option D: 7.2 × 10^-³⁰, 7 × 10^-³⁰, 7.6 × 10^-²⁵, 7.2 × 10^-²⁵.