Ask a New Question
Menu

Compare 364,879; 463,000; and 436,765 using scientific notation. Which number has the least value?(1 point) Responses 3.64879 × 10^5 3.64879 times 10 superscript 5 baseline 364,879 364,879 4.63 × 10^5 4.63 times 10 superscript 5 baseline 4.36765 × 10^5

11 answers

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

  1. Convert each number to scientific notation:

    • 364,879 = \(3.64879 \times 10^5\)
    • 463,000 = \(4.63 \times 10^5\) (which can also be written as \(4.63000 \times 10^5\))
    • 436,765 = \(4.36765 \times 10^5\)

  2. Now, we can compare them by looking at the coefficients since they all have the same exponent (10^5):

    • \(3.64879\) (for 364,879)
    • \(4.63\) (for 463,000)
    • \(4.36765\) (for 436,765)

  3. The coefficients are:

    • \(3.64879\) is less than \(4.36765\) and \(4.63\)

Therefore, since \(3.64879 < 4.36765 < 4.63\), the number with the least value is 364,879, which is represented as \(3.64879 \times 10^5\) in scientific notation.

Thank you so much you have no Idea how much this means

You're very welcome! I'm glad I could help. If you have any more questions or need further assistance, feel free to ask. Your understanding and learning are what matter most, and I'm here to support you!

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 × 10 10 1.2740876635 times 10 superscript 10 baseline 12,920,370,000 12,920,370,000 1.292037 × 10 10 1.292037 times 10 superscript 10 baseline 1.345763334 × 10 9

To compare the numbers 12,740,876,635; 1,345,763,334; and 12,920,370,000 in scientific notation, we will first convert each number:

  1. Convert each number to scientific notation:

    • 12,740,876,635: \[ 12,740,876,635 = 1.2740876635 \times 10^{10} \]
    • 1,345,763,334: \[ 1,345,763,334 = 1.345763334 \times 10^{9} \]
    • 12,920,370,000: \[ 12,920,370,000 = 1.292037 \times 10^{10} \]

  2. Now, compare the numbers:

    • For \( 1.2740876635 \times 10^{10} \) (12,740,876,635)
    • For \( 1.292037 \times 10^{10} \) (12,920,370,000)
    • For \( 1.345763334 \times 10^{9} \) (1,345,763,334)

Since the first two numbers have the same exponent (10^10), we will compare their coefficients:

  • \(1.2740876635\)
  • \(1.292037\)

Clearly, \(1.292037 > 1.2740876635\).

The third number, \(1.345763334 \times 10^{9}\) has a smaller exponent (10^9), which means it is less than both of the first two numbers.

  1. Conclusion: The greatest value among the three numbers is 12,920,370,000, which is represented as \(1.292037 \times 10^{10}\) in scientific notation.
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 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 7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline 7.6 × 10 − 25 > 6.7 × 10 − 52

To compare the two numbers \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\), we need to understand their scientific notation:

  1. Interpret the exponents:

    • \(10^{-25}\) and \(10^{-52}\) indicate how small each number is. The larger the negative exponent, the smaller the value of the number.
    • Since \(-25 > -52\), \(10^{-25}\) is much larger than \(10^{-52}\).

  2. Compare the two numbers:

    • For \(7.6 \times 10^{-25}\), even though the coefficient is \(7.6\), this is multiplied by a larger power of ten (less negative exponent).
    • For \(6.7 \times 10^{-52}\), while the coefficient \(6.7\) is also positive, this value is multiplied by a much smaller power of ten.

Since \(10^{-25}\) is greater than \(10^{-52}\), it follows that:

\[ 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \]

Thus, the correct statement is:

\(7.6 \times 10^{-25} > 6.7 \times 10^{-52}\).

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 − 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

To determine which set of numbers is arranged in descending order, we first need to compare the numbers provided in scientific notation. We will convert them into a form that makes comparisons easier.

  1. The numbers in scientific notation:

    • \(7 \times 10^{-30}\)
    • \(7.2 \times 10^{-25}\)
    • \(7.2 \times 10^{-30}\)
    • \(7.6 \times 10^{-25}\)

  2. Understanding the exponents:

    • The negative exponent indicates that the numbers are very small.
    • A larger negative exponent (like \(-25\) vs. \(-30\)) means the number is less small (or larger).
    • Therefore, \(10^{-25}\) (which corresponds to \(7.2\) and \(7.6\) with that exponent) is greater than \(10^{-30}\) (which corresponds to \(7\) and \(7.2\) with that exponent).

  3. Compare the numbers:

    • For \(10^{-25}\):
      • The two numbers are \(7.2 \times 10^{-25}\) and \(7.6 \times 10^{-25}\).
      • Between these, \(7.6 > 7.2\), so \(7.6 \times 10^{-25}\) is greater than \(7.2 \times 10^{-25}\).
    • For \(10^{-30}\):
      • The two numbers are \(7 \times 10^{-30}\) and \(7.2 \times 10^{-30}\).
      • Between these, \(7.2 > 7\), so \(7.2 \times 10^{-30}\) is greater than \(7 \times 10^{-30}\).

  4. Arranging in descending order:

    • Start with the largest exponent and coefficient:
      • \(7.6 \times 10^{-25}\)
      • \(7.2 \times 10^{-25}\)
      • \(7.2 \times 10^{-30}\)
      • \(7 \times 10^{-30}\)

Thus, the correct descending order is:

\(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\)

Looking at the options given, the set that matches this order is:

\(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\)

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

To determine which set of numbers is arranged in ascending order, let's first compare the numbers given in each option.

Convert all numbers to a common form for easier comparison:

  1. Decimal Numbers:

    • \(0.000325\)
    • \(0.00125\)
    • \(0.00225\)
    • \(0.00325\)

  2. Scientific Notation:

    • \(3.25 \times 10^{-4} = 0.000325\)
    • \(1.25 \times 10^{-3} = 0.00125\)
    • \(2.25 \times 10^{-3} = 0.00225\)
    • \(3.25 \times 10^{-3} = 0.00325\)

Arranging in Ascending Order:

Now, let's arrange the decimal numbers in ascending order based on their values:

  • \(0.000325\)
  • \(0.00125\)
  • \(0.00225\)
  • \(0.00325\)

The ascending order is:

  1. \(0.000325\)
  2. \(0.00125\)
  3. \(0.00225\)
  4. \(0.00325\)

Now, let’s check the sets provided:

  1. Set 1: \(0.00125, 0.00225, 0.000325, 0.00325\)

    • Not in ascending order.

  2. Set 2: \(0.00125, 0.00225, 0.000325, 0.00325\)

    • Not in ascending order.

  3. Set 3: \(0.000325, 0.00225, 0.00125, 0.00325\)

    • Not in ascending order.

  4. Set 4: \(0.000325, 0.00225, 0.00125, 0.00325\)

    • Not in ascending order.

  5. Set 5: \(3.25 \times 10^{-4}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-3}\)

    • This is also in ascending order as it corresponds to \(0.000325, 0.00125, 0.00225, 0.00325\).

  6. Set 6: \(3.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-4}, 1.25 \times 10^{-3}\)

    • Not in ascending order.

Conclusion:

The set that is arranged in ascending order is:

\(3.25 \times 10^{-4}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-3}\).