Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10^−8 meters wide by 2.5×10^−6 meters long. Use scientific notation to write the dimensions in millimeters.

Question

Note: 1 meter is equal to 1,000 millimeters.

(1 point)
Responses

1.25×10−11 by 2.5×10−9 millimeters
1.25 times 10 superscript negative 11 baseline by 2.5 times 10 superscript negative 9 baseline millimeters

1.25×10−6 by 2.5×10−4 millimeters
1.25 times 10 superscript negative 6 baseline by 2.5 times 10 superscript negative 4 baseline millimeters

1.25×10−10 by 2.5×10−8 millimeters
1.25 times 10 superscript negative 10 baseline by 2.5 times 10 superscript negative 8 baseline millimeters

1.25×10−5 by 2.5×10−3 millimeters

Answer 1

To convert the dimensions of the sticky note from meters to millimeters, you need to multiply each dimension by 1,000 (since there are 1,000 millimeters in a meter).

1. Width: \[ 1.25 \times 10^{-8} \text{ m} \times 1,000 = 1.25 \times 10^{-8} \text{ m} \times 10^3 = 1.25 \times 10^{-5} \text{ mm} \]

2. Length: \[ 2.5 \times 10^{-6} \text{ m} \times 1,000 = 2.5 \times 10^{-6} \text{ m} \times 10^3 = 2.5 \times 10^{-3} \text{ mm} \]

Thus, the dimensions in millimeters are:

\[ 1.25 \times 10^{-5} \text{ mm} \text{ by } 2.5 \times 10^{-3} \text{ mm} \]

The correct response is:

1.25×10^−5 by 2.5×10^−3 millimeters

1.25 times 10 superscript negative 5 baseline by 2.5 times 10 superscript negative 3 baseline millimeters.

Answer 2

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

3.99×103 seconds
3.99 times 10 cubed seconds

3.99×105 seconds
3.99 times 10 superscript 5 baseline seconds

0.399×106 seconds
0.399 times 10 superscript 6 baseline seconds

3.99×104 seconds

Answer 3

To find the total number of seconds that Jim's music library will play, we need to multiply the total number of songs by the average time of each song in seconds.

1. Number of songs: 1,900 songs

   • In scientific notation: \(1.9 \times 10^3\)

2. Average time per song: 3.5 minutes

   • Convert minutes to seconds: \[ 3.5 \text{ minutes} \times 60 \text{ seconds/minute} = 210 \text{ seconds} \]
   • In scientific notation: \(2.1 \times 10^2\)

3. Total time in seconds: To find the total duration, multiply the two values in scientific notation: \[ (1.9 \times 10^3) \times (2.1 \times 10^2) = 1.9 \times 2.1 \times 10^{3+2} \]

   First, calculate \(1.9 \times 2.1\): \[ 1.9 \times 2.1 = 3.969 \]

   Thus, we have: \[ 3.969 \times 10^{5} \]

   To express this in a more standard scientific notation (with two significant figures): \[ 3.969 \approx 3.97 \quad \text{(keeping significant figures)} \]

So, the total duration in scientific notation is: \[ 3.97 \times 10^5 \text{ seconds} \]

Hence, the closest response based on the provided options would lead us to use:

3.99×10^5 seconds
3.99 times 10 superscript 5 baseline seconds.

Answer 4

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+1025
6.02 plus 10 superscript 25 baseline

25×106.02
25 times 10 superscript 6.02 baseline

6.02×1025
6.02 times 10 superscript 25 baseline

6.02×25
6.02*25. not an exponet

Answer 5

The number \(6.02E25\) is in scientific notation, which represents \(6.02 \times 10^{25}\).

Given that the context is about the number of molecules in 100 moles, it's likely that \(6.02 \times 10^{25}\) refers to the total molecules (using Avogadro's number which is approximately \(6.02 \times 10^{23}\) molecules per mole multiplied by 100 moles).

The correct representation of the number in scientific notation is:

6.02×10^25
6.02 times 10 superscript 25 baseline.

This matches the third response option.

Answer 6

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

3.28×10−12
3.28 times 10 superscript negative 12 baseline

3.28+1012
3.28 plus 10 superscript 12 baseline

12×103.28
12 times 10 superscript 3.28 baseline

3.28×10^12

Answer 7

The number \(3.28E12\) is already in scientific notation, which is equivalent to \(3.28 \times 10^{12}\).

Therefore, the correct response in scientific notation is:

3.28×10^12
3.28 times 10 superscript 12 baseline.

This matches the fourth response option.

Answer 8

Sam is comparing the half-life of two isotopes of uranium. The half-life of Uranium-238 is 4.5×10^9 years. The half-life of Uranium-233 is 1.6×10^5 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

4×10^2.81
4 times 10 superscript 2.81 baseline

2.81+10^4
2.81 plus 10 superscript 4 baseline

2.81×10^4
2.81 times 10 superscript 4 baseline

2.81×10^−4

Answer 9

The number \(2.81E4\) is in scientific notation, which represents \(2.81 \times 10^{4}\).

Thus, the correct representation of this number in scientific notation is:

2.81×10^4
2.81 times 10 superscript 4 baseline.

This matches the third response option.

Answer 10

All correct. You're really good at this. Thank you!

Answer 11

Thank you for your kind words! I'm glad I could help. If you have any more questions or need assistance with anything else, feel free to ask!