Question

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 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 6.7 times 10 Superscript negative 52 Baseline 7.6 × 10−25 = 6.7 × 10−52

Answer 1

To compare the numbers \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\), we can first look at their scientific notation.

Both numbers are in the form \(a \times 10^b\). The key components to compare are the coefficients (7.6 and 6.7) as well as the exponents (-25 and -52).

1. Compare the exponents:

   • The exponent for \(7.6 \times 10^{-25}\) is -25.
   • The exponent for \(6.7 \times 10^{-52}\) is -52.
   • Since -25 is greater than -52, \(10^{-25}\) is larger than \(10^{-52}\).

2. Compare the overall values:

   • Since \(10^{-25} > 10^{-52}\), \(7.6 \times 10^{-25}\) must be greater than \(6.7 \times 10^{-52}\) regardless of the coefficients.

So, the correct statement is:

7.6 × 10−25 > 6.7 × 10−52

is true.

Answer 2

Which set of numbers is arranged in descending order?(1 point) Responses 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 × 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 × 10−30 , 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

Answer 3

To arrange the given set of numbers in descending order, we need to compare them based on their scientific notation, which is shown as \( a \times 10^b \).

Let's break down the numbers provided:

1. Compare Exponents:

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

2. Grouping by Exponents:

   • Both \(7.6 \times 10^{-25}\) and \(7.2 \times 10^{-25}\) have an exponent of -25. Between these two, \(7.6\) is greater than \(7.2\).
   • Both \(7.2 \times 10^{-30}\) and \(7 \times 10^{-30}\) have an exponent of -30. Between these two, \(7.2\) is greater than \(7\).

3. Overall Order:

   • The numbers with the larger exponent (-25) will be greater than those with the smaller exponent (-30). Thus, we can determine the order as follows:
     1. \(7.6 \times 10^{-25}\)
     2. \(7.2 \times 10^{-25}\)
     3. \(7.2 \times 10^{-30}\)
     4. \(7 \times 10^{-30}\)

Now, let's check which set is ordered correctly in the options provided:

The correct descending order is:

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

From the responses you've given, the first option matches this order:

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

This set is arranged in descending order.

Answer 4

Jim’s music library on his phone holds 1,900 songs. The songs have an average time of 3.5 minutes. Use scientific notation to find the total number of seconds the playlist will play. Express the answer to the exact decimal place.(1 point) Responses 0.399×106 seconds 0.399 times 10 superscript 6 baseline seconds 3.99×105 seconds 3.99 times 10 superscript 5 baseline seconds 3.99×103 seconds 3.99 times 10 cubed seconds 3.99×104 seconds

Answer 5

To find the total number of seconds that Jim's music library will play, we need to follow these steps:

1. Calculate the total playtime in minutes: \[ \text{Total time in minutes} = \text{Number of songs} \times \text{Average time per song} \] \[ \text{Total time in minutes} = 1900 \times 3.5 = 6650 \text{ minutes} \]

2. Convert the total playtime from minutes to seconds: Since there are 60 seconds in a minute: \[ \text{Total time in seconds} = 6650 \text{ minutes} \times 60 \text{ seconds/minute} \] \[ \text{Total time in seconds} = 399000 \text{ seconds} \]

3. Express the total in scientific notation: To express \(399000\) in scientific notation: \[ 399000 = 3.99 \times 10^5 \]

So, the total playtime of Jim's music library is \(3.99 \times 10^5\) seconds.

Thus, the correct response is: 3.99 × 10^5 seconds.

Answer 6

In chemistry class, Carlos calculated the number of molecules in 100 moles. The calculator displayed the number 6.02E25. What is the number of molecules in 100 moles in scientific notation?(1 point) Responses 6.02×25 6.02 times 25 6.02×1025 6.02 times 10 superscript 25 baseline 6.02+1025 6.02 plus 10 superscript 25 baseline 25×106.02

Answer 7

Carlos calculated the number of molecules in 100 moles, and the calculator displayed the number \(6.02E25\).

In scientific notation, \(6.02E25\) is equivalent to \(6.02 \times 10^{25}\).

Therefore, the correct response is:

6.02 × 10^25.

Answer 8

In government class, Nadia computed the amount of debt of the federal government after a third of it was paid in 1995. The calculator displayed the number 3.28E12. What is this number in scientific notation?(1 point) Responses 3.28×1012 3.28 times 10 superscript 12 baseline 3.28×10−12 3.28 times 10 superscript negative 12 baseline 12×103.28 12 times 10 superscript 3.28 baseline 3.28+1012

Answer 9

The calculator displayed the number \(3.28E12\), which is a representation in scientific notation. It means \(3.28 \times 10^{12}\).

So, the correct response is:

3.28 × 10¹².

Answer 10

Sam is comparing the half-life of two isotopes of uranium. The half-life of Uranium-238 is 4.5×109 years. The half-life of Uranium-233 is 1.6×105 years. He computed how much greater the half-life of Uranium-238 is than that of Uranium-233, and his calculator displayed the number 2.81E4. What is this number in scientific notation?(1 point) Responses 2.81×104 2.81 times 10 superscript 4 baseline 2.81+104 2.81 plus 10 superscript 4 baseline 4×102.81 4 times 10 superscript 2.81 baseline 2.81×10−4

Answer 11

The calculator displayed the number \(2.81E4\), which is expressed in scientific notation as \(2.81 \times 10^{4}\).

Thus, the correct response is:

2.81 × 10⁴.