Which set of numbers is arranged in descending order?(1 point)
Responses
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
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
7.6 × 10−25, 7.2 × 10−25, 7.2 × 10−30, 7 × 10−30
The set of numbers arranged in descending order is:
7.6 × 10^-25, 7.2 × 10^-25, 7.2 × 10^-30, 7 × 10^-30
To determine the set of numbers arranged in descending order, you need to compare the numbers and their exponents. In this case, you are given numbers expressed in scientific notation (x × 10^y), where x is the coefficient and y is the exponent.
Let's analyze the given options:
Option 1: 7.2 × 10^(-30), 7 × 10^(-30), 7.6 × 10^(-25), 7.2 × 10^(-25)
Option 2: 7.6 × 10^(-25), 7.2 × 10^(-25), 7.2 × 10^(-30), 7 × 10^(-30)
Option 3: 7.6 × 10^(-25), 7.2 × 10^(-30), 7.2 × 10^(-25), 7 × 10^(-30)
Option 4: 7 × 10^(-30), 7.2 × 10^(-25), 7.2 × 10^(-30), 7.6 × 10^(-25)
To compare the numbers, start by comparing the coefficients. The larger the coefficient, the larger the number. If the coefficients are the same, compare the exponents. The smaller the exponent, the larger the number.
In option 1, both 7.2 × 10^(-30) and 7 × 10^(-30) have the same coefficient (7.2 and 7), so now compare the exponents. 10^(-30) is larger than 10^(-25), so option 1 is not in descending order.
In option 2, 7.6 × 10^(-25) has a larger coefficient than 7.2 × 10^(-25), so it comes first. The exponents are the same, so we move on to the next pair. 7.2 × 10^(-30) has a smaller exponent than 7 × 10^(-30), so it comes next. Therefore, option 2 is arranged in descending order.
In option 3, the first pair is the same as option 2, so it is already not in descending order.
In option 4, 7.2 × 10^(-25) has a larger coefficient than 7 × 10^(-30), so it comes first. The exponents for the next pair are different, so we can directly compare them. 10^(-30) is smaller than 10^(-25), so 7.6 × 10^(-25) comes next. Therefore, option 4 is arranged in descending order.
Based on the analysis, the set of numbers that is arranged in descending order is option 4: 7 × 10^(-30), 7.2 × 10^(-25), 7.2 × 10^(-30), 7.6 × 10^(-25).