Algebra 2!!! Please help! I am confused and have something due in an hour!

Question

The diameter of our solar system (depending on how you define “solar system”) is about 

8,980,000,000,000 kilometers. 

The distance from our solar system to the nearest star, Proxima Centauri, is about 

39,900,000,000,000,000 kilometers. 

A light-year is the distance light travels in one year, and it is equal to about 

9,460,000,000,000 kilometers. 

a) Write each of these numbers in scientific notation. Explain how you got your answers, and explain why you know that your method works. 

b) You’d like to both know the end-to-end distance within the solar system and the distance to Proxima Centauri in light-years. Using your scientific notation numbers, convert these distances. What is the ratio of the solar system’s length to the Proxima Centauri distance? 

c) Light travels at 300,000 kilometers per second. Write this rate in scientific notation. When Proxima Centauri sends out light at that speed, how long does it take to reach our solar system? Can you convert to minutes, hours, days, or years? Does your answer in years correspond to the distance in light-years from our solar system to Proxima Centauri? Why or why not?

Answer 1

Hi Carly F...WOW!! You have a pretty big assignment.

I'm here to help.

I'm going to begin with helping you out with your first problems...give you the understanding of how you began understanding about scientific notation and why it is helpful.

This also brings into several properties of Algebra.

So let's begin with understanding about scientific notation.

As you problem begin, it states the diameter of our solar system is:

8,980,000,000,000 kilometers THAT'S A LOT OF NUMBERS, ESPECIALLY ZEROS!

It would be a drag, to much of a problem to write these numbers and zeros again, and again and again. However, it is an important number.

A good way to think about this is when we talk we use contractions instead of entire words.

Here are some examples: Some people will say or write I cannot go to the concert.

Some people will say or write I can't go to the concert.

They both mean the same thing.

Here's another example: Some people will say or write I am going to the movies.

Some people will say or write I'm going to the movies

They both mean the same thing.

So just like grammar, scientific notation is just shortening the large numbers into a shorter form, BUT not changing the value.

Here are the rules and how to apply them.

1st: take the known real numbers, place a decimal point to the right of the first real number.

2nd: Count the number of places after the decimal points toward the right until the last place.

3rd: Write the real number with the decimal point.

4th: Place a 'times' symbol, multiplication sign after the real number.

5th: After the 'times' symbol write the number 10.

6th: Writing as an exponent, the number of places you counted going to the right to the end of the number.

Here is an example, starting out with a simple number. The number is 1,200 Follow the rules:

1st: Place a decimal point after the 1st real number: decimal point between the 1 and the 2 1.2

2nd: After the decimal count the numbers going to the right to the end which is '3'

3rd: Write the decimal number: 1.2

4th: Put the 'times' symbol: 1.2 x

5th: After the times write the number 10: 1.2 x 10

6th: As an exponent write the number of times you counted to the right: 1.2 x 10³

So, the number 1,200 is the same number in scientific notation as 1.2 x 10³

[HINT: To count the place to the right, place your pen/pencil on the decimal point and use you pen/pencil to count each space going to the right to the end of the number.

HERE'S ANOTHER EXAMPLE: 2,030,000 let's follow the rules

1st: 2.03

2nd: Staring at the decimal after the 2, count to the right. Which turns out to be 6

3rd: 2.03

4th: 2.03 x

5th: 2.03 x 10

6th: 2.03 x 10⁶

So the number 2,030,000 is the same as 2.03 x 10⁶ in scientific notation

So I'll help you with the first part of you problem:

8,980,000,000,000 kilometers Follow the rules!!

1st: 8.98

2nd: after the decimal after the 8 count: Which is 12

3rd: 8.98

4th: 8.98 x

5th: 8.98 x 10

6th: 8.98 x 10¹²

So the number 8,980,000,000,000 is the same as 8.98 x 10¹² in scientific notation

We would end up writing 8.98 x 10¹² kilometers is the same as 8,980,000,000,000 kilometers

Writing in scientific notation is a whole easier than writing the entire number.

Some additional rules to follow:

ALWAYS WRITE THE UNITS WITH THE SCIENTIFIC NOTATION: inches, feet, kilometers, etc.

Here is why we add the exponent as it follow the EXPONENT RULES like this:

10 = 1.0 x 10¹

100 = 1.0 x 10²

1,000 = 1.0 x 10³

10,000 = 1.0 x 10⁴

100,000 = 1.0 x 10⁵

1,000,000 = 1.0 x 10⁶

Do you see how there is a pattern?

Hope this helps. You should be able to complete the rest of your assignment.

Let me know if you need any further assistance.

I am here to help.

You can contact me by way of Wyzant.

I also tutor online.

J