Compare Very Large and Very Small Numbers Quick Check
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Question
Which set of numbers is arranged in descending order?(1 point)
Responses
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
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
7.6 × 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
To compare the set of numbers and arrange them in descending order, we look at the coefficient of each number first. The coefficient is the number in front of the scientific notation.
Comparing the coefficients:
7.6 > 7.2 > 7
Next, we compare the exponents (powers of 10):
10^-25 > 10^-30
Arranging the set in descending order based on the comparisons:
7.6 × 10^-25
7.2 × 10^-25
7.2 × 10^-30
7 × 10^-30
Therefore, 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 compare the set of numbers and determine which one is arranged in descending order, we need to understand the concept of exponent notation.
In exponent notation, a number is expressed as a product of a coefficient and a power of 10. The coefficient value is a number between 1 and 10, and the power of 10 determines the scale or magnitude of the number.
To compare the numbers, we need to focus on the exponents. The larger the exponent, the smaller the number.
Let's analyze the options:
- Option 1: 7.6 × 10^(-25), 7.2 × 10^(-30), 7.2 × 10^(-25), 7 × 10^(-30)
- Option 2: 7.2 × 10^(-30), 7 × 10^(-30), 7.6 × 10^(-25), 7.2 × 10^(-25)
- Option 3: 7 × 10^(-30), 7.2 × 10^(-25), 7.2 × 10^(-30), 7.6 × 10^(-25)
- Option 4: 7.6 × 10^(-25), 7.2 × 10^(-25), 7.2 × 10^(-30), 7 × 10^(-30)
To determine the descending order, we compare the exponents from left to right.
Looking at option 1, we can see that the first exponent (-25) is larger than the second exponent (-30). Therefore, option 1 is not in descending order.
Analyzing option 2, we can see that the exponents are in descending order (-30, -30, -25, -25). Therefore, option 2 is arranged in descending order.
Options 3 and 4 also have the exponents out of order, so they are not arranged in descending order.
Thus, the correct answer is:
- Option 2: 7.2 × 10^(-30), 7 × 10^(-30), 7.6 × 10^(-25), 7.2 × 10^(-25)