Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10−8

Question

meters wide by 2.5×10−6
meters long. Use scientific notation to write the dimensions in millimeters.

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

(1 point)
Responses

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

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

1.25×10−5
by 2.5×10−3
millimeters
1.25 times 10 superscript negative 5 baseline by 2.5 times 10 negative cubed 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

Answer 1

To convert the dimensions of the sticky note from meters to millimeters, you multiply the measurements in meters by 1,000, since 1 meter is equal to 1,000 millimeters.

1. For the width: \[ 1.25 \times 10^{-8} \text{ meters} \times 1000 \text{ mm/m} = 1.25 \times 10^{-8} \times 10^{3} \text{ mm} = 1.25 \times 10^{-5} \text{ mm} \]

2. For the length: \[ 2.5 \times 10^{-6} \text{ meters} \times 1000 \text{ mm/m} = 2.5 \times 10^{-6} \times 10^{3} \text{ mm} = 2.5 \times 10^{-3} \text{ mm} \]

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 from the options provided is:

1.25×10−5 by 2.5×10−3 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

3.99×104
seconds
3.99 times 10 superscript 4 baseline seconds

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

Answer 3

To find the total play time of Jim's music library in seconds, we first need to calculate the total play time in minutes and then convert that to seconds.

1. Calculate total play time in minutes: \[ \text{Total minutes} = \text{Number of songs} \times \text{Average time per song} \] \[ \text{Total minutes} = 1,900 \text{ songs} \times 3.5 \text{ minutes/song} = 6,650 \text{ minutes} \]

2. Convert total play time to seconds: Since there are 60 seconds in a minute, we multiply the total minutes by 60: \[ \text{Total seconds} = 6,650 \text{ minutes} \times 60 \text{ seconds/minute} = 399,000 \text{ seconds} \]

3. Convert to scientific notation: The total seconds can be expressed in scientific notation as: \[ 399,000 = 3.99 \times 10^{5} \text{ seconds} \]

Thus, the correct response from the options provided is:

3.99×10^5 seconds.

Answer 4

n 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

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 times 25

6.02+1025

Answer 5

In chemistry, the number of molecules in one mole is represented by Avogadro's number, which is approximately \(6.02 \times 10^{23}\) molecules per mole.

To find the number of molecules in 100 moles:

\[ 100 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mole} = 6.02 \times 100 \times 10^{23} \text{ molecules} \]

Calculating \(6.02 \times 100\):

\[ 6.02 \times 100 = 602 \]

Now, we express \(602\) in scientific notation:

\[ 602 = 6.02 \times 10^2 \]

So, combining this with the \(10^{23}\):

\[ 6.02 \times 10^2 × 10^{23} = 6.02 \times 10^{2 + 23} = 6.02 \times 10^{25} \text{ molecules} \]

Thus, the correct number of molecules in 100 moles in scientific notation is:

6.02×10^25.

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+1012
3.28 plus 10 superscript 12 baseline

3.28×1012
3.28 times 10 superscript 12 baseline

12×103.28
12 times 10 superscript 3.28 baseline

3.28×10−12

Answer 7

The notation \(3.28E12\) is equivalent to \(3.28 \times 10^{12}\) in scientific notation. The "E" stands for exponent, which is a common representation in calculators and programming to denote powers of ten.

Thus, the correct representation of the number \(3.28E12\) in scientific notation is:

3.28×10^{12}.

Answer 8

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

4×102.81
4 times 10 superscript 2.81 baseline

2.81×10−4
2.81 times 10 superscript negative 4 baseline

2.81+104

Answer 9

The notation \(2.81E4\) is equivalent to \(2.81 \times 10^{4}\) in scientific notation. The "E" represents "exponent," indicating a power of ten.

Thus, the correct representation of the number \(2.81E4\) in scientific notation is:

2.81×10^{4}.