do these questions make sense?

M

mathguy

New member
Joined
Jun 3, 2011
Messages
8
Hi all, I was wondering what you think of this:

Express (4.1)(10^2) in standard form. Is it not already?
I thought standard form is (n)(10^x)

Also, how would you express 5^4 in standard form?


I am soo confused... thanks.
 



We call this form "scientific notation".

(4.1)(10^2) is scientific notation for the number 410.

There are different conventions for writing scientific notation, yet in beginning classes a multiplication sign is most commonly used.

(NOTE: I'm renaming your exponent symbol from x to k, since x looks too much like ×)

n × 10^k

where n is some number between 1 and 10 (n can actually equal 1; otherwise, it must be less than 10) and the exponent k is the number of positions that the decimal point must shift.

410 = 4.1 × 10^2

Here, k = 2, so we shift the decimal point two positions -- from 4.1 to 410.



As for writing the number 5^4 in scientific notation, start by calculating the value of 5^4.

Then, shift the decimal point k places to get your n between 1 and 10.



EG:

Write 3^7 in scientific notation

3^7 = 2187

To get a number between 1 and 10, we must shift the decimal point three places.

So, k = 3 and n = 2.187

In scientific notation, 3^7 is written as 2.187 × 10^3



The usefulness of scientific notation is realized when writing very big (or very small) numbers. For example, the distance that light travels in one year is about 5,870,000,000,000 meters. Who wants to write all of those zeros again and again?

Scientific notation makes this big number more compact:

5.87 × 10^12 meters

 
Thanks, mmm4444bot. I now understand how to get a number in scientific notation. Just to confirm though, if a number is in the form nx10^n, it is already in standard form, correct?

If a teacher writes that I have to write 4.1 x 10^2 in standard form, what would I do?
 
Two other thoughts.

In scientific notation, the number of digits to the right of the decimal point indicates the degree of precision. So if your number is 410, the proper way to show that in scientific notation is 4.10 * 10[sup:3o4bcdfc]2[/sup:3o4bcdfc], not 4.1 * 10[sup:3o4bcdfc]2[/sup:3o4bcdfc], which would mean 410 plus or minus 5.

I am also worried about "standard notation" in your problem statement. "Scientific notation" is clear enough, but "standard notation?" Standard among what group? Is it possible that the problem is asking you to turn 4.1 * 10[sup:3o4bcdfc]2[/sup:3o4bcdfc] into 410, etc.? This concern may disappear given be context; if for example you are currently studying scientific notation, I think it is safe to assume "standard notation" = "scientific notation." If on the other hand you are currently studying exponents, I am not sure how to interpret "standard notation." Is "standard notation" the term used in the statement of the problem, or was that your translation?
 
I "think" the standard notation is analogous to decimal notation.
 


The name "standard form" is British English for "scientific notation". I based my post on an assumption that mathguy is studying with the Brits.

I did not bring up significant digits, but those rules are good to learn, too, especially where precision is important (eg: chemistry, astronomy, physics).

And, yes, if somebody asks to put 4.1 × 10^2 into standard form (aka scientific notation), then that is a "trick" question because the given expression is already written in standard form.

That question would make more sense if the given expression were instead something like:

0.41 × 10^2 or 41 × 10^2

Standard form would then be:

4.1 × 10 or 4.1 × 10^3, respectively.

Following is an example where k is negative. In other words, the decimal point must shift to the left instead of the right:

0.000456 = 4.56 × 10^(-4)

8-)

 
polygonjordy said:
Interested to know your teachers response

Me too! :)
Click to expand...

If my assumption about British English is incorrect, I should post a retraction or something.

 
You must log in or register to reply here.
Top