Scientific Notation and ratio

[kreeto]

Hello all!
This is my first time posting after I did a quick google search of math forums. Never used a forum before. I am so stuck on this question, so here goes.
question: If an atom has a diameter of 4 X 10^-8cm and its nucleus has a diameter of 8 X 10^-13cm, find the ratio of the diameter of the nucleus to the diameter of the atom.

So far I have broken it down to 4/8 x 10^-8/10^-13 and have solved it down to 4/8 X 10⁵.
But that's where I get stuck. please help me!

Kree!

 

[tkhunny]

nucleus / atom ==> Smaller / larger ==> It will be less than 1. Your answer of 10^5 can't be right. Always keep an eye out for reasonable results.

As you have it: 4/8 10E5 = 1/2 10E5 = .5 10E5 = 5 10E4 -- Lot's of ways to write it.

Okay, now how SHOULD it be? nucleus / atom ==> Smaller / larger ==>

 

[topsquark]

This notation is killing me.

Instead, let's write it this way:
\(\displaystyle \dfrac{4 \times 10^{-13} }{8 \times 10^{-8} } = \dfrac{4}{8} \cdot \dfrac{10^{-13}}{10^{-8}} = 0.5 \times 10^{-13 + 8} = 0.5 \times 10^{-5}\)

\(\displaystyle = 5 \times 10^{-6}\)

-Dan

 

[kreeto]

This notation is killing me.

Instead, let's write it this way:
\(\displaystyle \dfrac{4 \times 10^{-13} }{8 \times 10^{-8} } = \dfrac{4}{8} \cdot \dfrac{10^{-13}}{10^{-8}} = 0.5 \times 10^{-13 + 8} = 0.5 \times 10^{-5}\)

\(\displaystyle = 5 \times 10^{-6}\)

-Dan

I really appreciate your fast response. like I said this is my first time posting here I don't know exactly how to use this. do I flip the exponents or was that a typo? also, how would I write the fractions like you did I am sorry to ask I just want to make it easier on the eyes.

 

[JeffM]

Do NOT worry at this stage about using LaTeX, the software used by this site to render pretty math notation. The software is persnickety, and you need to concentrate on math, not scripting. You can work with fractions in line using / and parentheses.

Going back to your very first post:

[MATH]\text {diameter of the atom} = 4 * 10^{-8}.[/MATH]
[MATH]\text {diameter of the nucleus} = 8 * 10^{-13}.[/MATH]
So ratio of nucleus to atom is nucleus / atom, which gives

[MATH](8 * 10^{-13}) / (4 * 10^{-8}) = (8/4) * (10^{-13}/10^{-8}) = 2 * (10^{-13}/10^{-8}).[/MATH]
Now, to use scientific notation, you need to KNOW well all the laws of exponents. In this case you need to know

[MATH]\text {If } a > 0, \text { then } a^b/a^c = a^{b-c}. [/MATH]
[MATH]\text {So, } 10^{-13}/10^{-8} = 10^{\{-13 - (-8)\}} = 10^{(-13 + 8)} = 10^{(-5)}. [/MATH]
[MATH]\text {Thus, the answer is } 2 * 10^{(-5)}.[/MATH]

 

[Harry_the_cat]

Diameter of nucleus : Diameter of atom
= 8 x 10^-13 : 4 x 10^-8
= 2 x 10^-13 : 1 x 10^-8 …. dividing both sides by 4
= 2 : 1 x 10⁵ …. multiplying each side by 10¹³
= 2 : 100 000
= 1 : 50 000 or 1 : 5 x 10⁴ if scientific notation is required

I believe a "ratio" should be expressed with a ":" sign.

 

[JeffM]

Diameter of nucleus : Diameter of atom
= 8 x 10^-13 : 4 x 10^-8
= 2 x 10^-13 : 1 x 10^-8 …. dividing both sides by 4
= 2 : 1 x 10⁵ …. multiplying each side by 10¹³
= 2 : 100 000
= 1 : 50 000 or 1 : 5 x 10⁴ if scientific notation is required

I believe a "ratio" should be expressed with a ":" sign.

But you need to divide both sides by ten to the minus 13.

 

[Harry_the_cat]

But you need to divide both sides by ten to the minus 13.

Multiplying by 10¹³ is the same thing!

 

[JeffM]

Multiplying by 10¹³ is the same thing!

Still on first cup of coffee!

 

[Harry_the_cat]

Go make yourself another one!

 

[kreeto]

thank you all soo much!!