Question

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. 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 from meters to millimeters, we need to multiply the measurements in meters by 1,000 because 1 meter is equal to 1,000 millimeters.

1. Convert the width: \[ 1.25 \times 10^{-8} \text{ meters} \times 1,000 \text{ mm/meter} = 1.25 \times 10^{-8} \times 10^{3} \text{ mm} = 1.25 \times 10^{-5} \text{ mm} \]

2. Convert the length: \[ 2.5 \times 10^{-6} \text{ meters} \times 1,000 \text{ mm/meter} = 2.5 \times 10^{-6} \times 10^{3} \text{ mm} = 2.5 \times 10^{-3} \text{ mm} \]

Thus, the dimensions of the sticky note 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.

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 × 10 4 seconds 3.99 times 10 superscript 4 baseline seconds 3.99 × 10 5 seconds 3.99 times 10 superscript 5 baseline seconds 0.399 × 10 6 seconds 0.399 times 10 superscript 6 baseline seconds 3.99 × 10 3 seconds

Answer 3

To find the total number of seconds the playlist will play, we first need to compute the total duration of the songs in minutes and then convert that to seconds.

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

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

3. Express in scientific notation: \[ 399,000 = 3.99 \times 10^5 \text{ seconds} \]

The correct response is: 3.99 × 10 5 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 × 25 6.02 times 25 6.02 + 10 25 6.02 plus 10 superscript 25 baseline 6.02 × 10 25 6.02 times 10 superscript 25 baseline 25 × 10 6.02

Answer 5

The notation "6.02E25" is equivalent to "6.02 × 10^25" in scientific notation.

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

6.02 × 10^25.

The correct response is: 6.02 × 10 25 (6.02 times 10 superscript 25 baseline).

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

Answer 7

The notation "3.28E12" is equivalent to "3.28 × 10^12" in scientific notation.

Thus, the number Nadia computed is:

3.28 × 10^12.

The correct response is: 3.28 × 10 12 (3.28 times 10 superscript 12 baseline).

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 notation "2.81E4" is equivalent to "2.81 × 10^4" in scientific notation.

Thus, the number Sam computed is:

2.81 × 10^4.

The correct response is: 2.81 × 10 4 (2.81 times 10 superscript 4 baseline).