Scientific Notation Portfolio
Math 8 Q1 (Pre-Algebra) / Scientific Notation
step 1: Come up with a question you are genuinely curious about and want to try to
make sense of: (i.e how big…, how fast…, how many…, how far…, etc )
Step 2: Figure out a way to make a comparison that could make the answer to
your question more comprehensible
step 3: What is your comparison going to be about? Explain why you are interested in
this/why it would be a useful comparison.
Step 3b: Do the mathematics to make the comparison. This will require calculations
in scientific notation and, likely, estimation.
● Be sure to express your quantity in scientific notation and then make your
comparison
● Keep a careful record of your mathematics and thinking.
● Annotate (explain with notes) your calculations so that anyone looking at your
work can follow your thinking.
Step 1: Question
How big is the universe in relation to the size of our solar system?
Step 2: Comparison
To make the answer to my question more comprehensible, I will compare the size of the universe to the size of our solar system.
Step 3: Comparison
I am interested in this comparison because it will provide a scale of the vastness of the universe compared to our own solar system. It will help us understand the enormity of the universe and our place within it.
Step 3b: Mathematics
1. Size of our solar system:
The average distance from the Earth to the Sun is approximately 93 million miles.
2. Size of the universe:
The observable universe has a diameter of about 93 billion light-years.
To compare these values, I will convert them to scientific notation.
1. Size of our solar system:
93 million miles = 9.3 x 10^7 miles
2. Size of the universe:
93 billion light-years = 9.3 x 10^10 light-years
Now, we can compare the size of the universe to our solar system:
9.3 x 10^10 light-years / 9.3 x 10^7 miles
To divide these numbers, we subtract the exponents:
9.3 x 10^(10-7) light-years / miles
= 9.3 x 10^3 light-years / miles
Therefore, the universe is approximately 9.3 thousand times larger than our solar system.
This calculation helps us grasp the immense size of the universe compared to our relatively small solar system. It highlights the vastness and magnitude of the cosmos.
Step 1: Question
How fast does light travel compared to the speed of sound?
Step 2: Comparison
To make the answer more comprehensible, I will compare the time it takes for light and sound to travel a specific distance.
Step 3: Comparison Explanation
I am interested in this comparison because it helps me understand the relative speeds of light and sound, which are fundamental concepts in physics. It is also a useful comparison because it provides perspective on the vast difference in speed between these two phenomena.
Step 3b: Mathematics and Calculation
To make the comparison, I will use the speed of light and sound in scientific notation and then calculate the time it takes for them to travel a specific distance.
Speed of Light: Approximately 299,792,458 m/s (expressed in scientific notation as 2.9979 x 10^8 m/s)
Speed of Sound: Approximately 343 m/s (expressed in scientific notation as 3.43 x 10^2 m/s)
Let's assume we want to compare the time it takes for light and sound to travel 1 kilometer (1000 meters).
Time taken by light: Distance / Speed of Light
= 1000 m / (2.9979 x 10^8 m/s)
= 3.33564 x 10^-6 seconds
Time taken by sound: Distance / Speed of Sound
= 1000 m / (3.43 x 10^2 m/s)
= 2.91439 seconds
So, it takes approximately 3.33564 x 10^-6 seconds for light to travel 1 kilometer, while it takes around 2.91439 seconds for sound to cover the same distance.
Annotations:
- I used the speed of light as 2.9979 x 10^8 m/s and the speed of sound as 3.43 x 10^2 m/s.
- I divided the distance of 1000 meters by the respective speeds to find the time taken.
- The resulting time for light is 3.33564 x 10^-6 seconds, and for sound is 2.91439 seconds.
Step 1: Question
How big is the observable universe?
Step 2: Comparison
I will compare the size of the observable universe to the size of our solar system.
Step 3: Comparison and Interest
I am interested in this comparison because it can help us visualize the immense scale of the universe. Our solar system is already vast, with the Sun at its center and various planets, asteroids, and comets orbiting around it. If we can see how much bigger the observable universe is compared to our solar system, it can give us a better understanding of just how tiny and insignificant our immediate neighborhood in space really is.
Step 3b: Mathematics and Calculations
To make this comparison, I will express the size of the observable universe and our solar system in scientific notation and then compare them.
The observable universe is estimated to have a radius of about 46.5 billion light-years. To express this in scientific notation, we need to convert it to meters and then divide by the speed of light (299,792,458 meters per second).
46.5 billion light-years = 4.38014 x 10^26 meters
Our solar system is commonly measured using the distance from the Sun to its farthest planet, Neptune. Neptune's average distance from the Sun is about 4.50 billion kilometers. To convert this to meters, we multiply by 1,000,000.
4.50 billion kilometers = 4.50 x 10^12 meters
Now, let's compare the two quantities:
Observable Universe: 4.38014 x 10^26 meters
Solar System: 4.50 x 10^12 meters
As we can see, the size of the observable universe is much larger than the size of our solar system. The difference in magnitude is enormous, with the observable universe being approximately 10^14 times larger than our solar system.
This comparison helps us grasp the vastness of the universe beyond our immediate surroundings, highlighting the scale at which cosmic objects and distances operate.