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Compare 364,879; 463,000; and 436,765 using scientific notation. Which number has the least value?(1 point)

Responses

364,879
364,879

3.64879 ×105
3.64879 times 10 superscript 5 baseline

4.63 ×105
4.63 times 10 superscript 5 baseline

4.36765 ×105
4.36765 times 10 superscript 5 baseline

11 answers

To compare the numbers 364,879; 463,000; and 436,765 using scientific notation:

  1. 364,879 can be written as \( 3.64879 \times 10^5 \)
  2. 463,000 can be written as \( 4.63 \times 10^5 \)
  3. 436,765 can be written as \( 4.36765 \times 10^5 \)

Now, we can compare these values in scientific notation:

  • \( 3.64879 \times 10^5 \)
  • \( 4.63 \times 10^5 \)
  • \( 4.36765 \times 10^5 \)

When comparing numbers in scientific notation, we first look at the exponent on 10; since all three have the same exponent of \( 10^5 \), we only need to compare the coefficients:

  • \( 3.64879 \)
  • \( 4.63 \)
  • \( 4.36765 \)

Among the coefficients, \( 3.64879 \) is the smallest.

Thus, the number with the least value is 364,879 or \( 3.64879 \times 10^5 \).

so which one i cant answer both

Apologies for any confusion! Here's the clear answer:

The number with the least value among 364,879, 463,000, and 436,765 is:

364,879 (which is \( 3.64879 \times 10^5 \) in scientific notation).

Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?(1 point)
Responses

1.2740876635×1010
1.2740876635 times 10 superscript 10 baseline

1.345763334×109
1.345763334 times 10 superscript 9 baseline

1.292037×1010
1.292037 times 10 superscript 10 baseline

12,920,370,000
12,920,370,000

To compare the numbers 12,740,876,635, 1,345,763,334, and 12,920,370,000 using scientific notation:

  1. 12,740,876,635 can be written as: \[ 1.2740876635 \times 10^{10} \]

  2. 1,345,763,334 can be written as: \[ 1.345763334 \times 10^{9} \]

  3. 12,920,370,000 can be written as: \[ 1.292037 \times 10^{10} \]

Now let's compare the scientific notation:

  • \( 1.2740876635 \times 10^{10} \)
  • \( 1.345763334 \times 10^{9} \) (this has a lower exponent of \( 10^{9} \))
  • \( 1.292037 \times 10^{10} \)

Since \( 1.345763334 \times 10^{9} \) has a lower exponent, it is definitely smaller than both of the others.

Now let's compare the two with the same exponent \( 10^{10} \):

  • \( 1.2740876635 \)
  • \( 1.292037 \)

Since \( 1.292037 \) is greater than \( 1.2740876635 \), that means 12,920,370,000 (or \( 1.292037 \times 10^{10} \)) has the greatest value.

So, the answer is: 12,920,370,000 (or \( 1.292037 \times 10^{10} \)).

Compare 7.6 × 10−25 and 6.7 × 10−52. Which statement is true?(1 point)
Responses

7.6 × 10−25 > 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10−25 ≤ 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is less than or equal to 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10−25 < 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10−25 = 6.7 × 10−52

To compare \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we can analyze their scientific notations.

  1. Exponents:

    • \( 10^{-25} \) is greater than \( 10^{-52} \) because a smaller (more negative) exponent means a smaller number.

  2. Comparing the two numbers:

    • When you have a number with a higher exponent, it will be greater, even if the coefficient (the first part of the number) is smaller.
    • Therefore, \( 7.6 \times 10^{-25} \) will be much larger than \( 6.7 \times 10^{-52} \).

This leads to the conclusion:

The true statement is: \( 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \).

Question
Which set of numbers is arranged in descending order?(1 point)
Responses

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

7.2 × 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 × 10−30, 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

7.6 × 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 determine which set of numbers is arranged in descending order, we need to compare the values based on their scientific notation.

Let's rewrite each number clearly for comparison:

  1. \( 7 \times 10^{-30} \)
  2. \( 7.2 \times 10^{-25} \)
  3. \( 7.2 \times 10^{-30} \)
  4. \( 7.6 \times 10^{-25} \)

Now let's analyze the sets one by one:

  1. Set: \( 7 \times 10^{-30}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7.6 \times 10^{-25} \)

    • Descending order: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30} \) (not in correct order)

  2. Set: \( 7.2 \times 10^{-30}, 7 \times 10^{-30}, 7.6 \times 10^{-25}, 7.2 \times 10^{-25} \)

    • Descending order: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30} \) (not in correct order)

  3. Set: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-30}, 7.2 \times 10^{-25}, 7 \times 10^{-30} \)

    • Descending order: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30} \) (correct order)

  4. Set: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30} \)

    • Descending order: \( 7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30} \) (correct order)

Both sets 3 and 4 are arranged in descending order, but to keep it simple, the first set that provides an example of descending order is:

7.6 × 10−25, 7.2 × 10−25, 7.2 × 10−30, 7 × 10−30

So, the answer is:

7.6 × 10−25, 7.2 × 10−25, 7.2 × 10−30, 7 × 10−30 (This is option 4).

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

0.00125, 0.00225, 0.000325, 0.00325
0.00125, 0.00225, 0.000325, 0.00325

0.000325, 0.00225, 0.00125, 0.00325
0.000325, 0.00225, 0.00125, 0.00325

3.25 × 10−3, 2.25 × 10−3, 3.25 × 10−4, 1.25 × 10−3
3.25 times 10 Superscript negative 3 Baseline , 2.25 times 10 Superscript negative 3 Baseline , 3.25 times 10 Superscript negative 4 Baseline , 1.25 times 10 Superscript negative 3 Baseline

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

To determine which set of numbers is arranged in ascending order, we need to evaluate each set.

Set Evaluations:

  1. Set: 0.00125, 0.00225, 0.000325, 0.00325

    • Comparison:
      • 0.000325 < 0.00125 < 0.00225 < 0.00325
    • Not in ascending order.

  2. Set: 0.000325, 0.00225, 0.00125, 0.00325

    • Comparison:
      • 0.000325 < 0.00125 < 0.00225 < 0.00325
    • Not in ascending order.

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

    • Convert to decimal:
      • \( 3.25 \times 10^{-3} = 0.00325 \)
      • \( 2.25 \times 10^{-3} = 0.00225 \)
      • \( 3.25 \times 10^{-4} = 0.000325 \)
      • \( 1.25 \times 10^{-3} = 0.00125 \)
    • Order is:
      • 0.000325 < 0.00125 < 0.00225 < 0.00325
    • Not in ascending order.

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

    • Convert to decimal:
      • \( 3.25 \times 10^{-4} = 0.000325 \)
      • \( 1.25 \times 10^{-3} = 0.00125 \)
      • \( 2.25 \times 10^{-3} = 0.00225 \)
      • \( 3.25 \times 10^{-3} = 0.00325 \)
    • Order is:
      • 0.000325 < 0.00125 < 0.00225 < 0.00325
    • This is in ascending order.

Conclusion:

The set that is arranged in ascending order is:

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