Concerning Significant Figures.

[Mozart]

Hello
I have 2 questions about sig figs that have been bothering me.

I worked out this calculation: (3.652 x 108) (42.8 x 10-6)

My answer was 67524.0192. I figured that since there is a 6 in the second parenthesis my answer should be only 1 sig fig. So I expressed it as 7 x 10^4 Can you even write scientific notaion like that without any decimals? It seems odd.

Another problem I have concerns rounding off. If for instance I have my final answer as 3.5673 and I have to use only 3 sig figs do I round from the 6 and change my answer to 3.60 or do I round from the 7 and change my answer to 3.56?

Thank you.

 

[Tide]

The number in the second set of parentheses has 3 significant digits. You don't count the exponent.

 

[Mozart]

Oh that's not an exponent. It does look like one though. It's (42.8 x 10 minus 6) and I just realized how I messed up the order of operations in my calculation. The result should be 166443.552 so would it be 2 x 10^5?

 

[andrevdh]

If I attempt your calculation
$$(3.652 \times 10^8)(42.8 \times 10^{-6})$$
I get
$$15630.56$$
?

 

[HallsofIvy]

Oh that's not an exponent. It does look like one though. It's (42.8 x 10 minus 6) and I just realized how I messed up the order of operations in my calculation. The result should be 166443.552 so would it be 2 x 10^5?

Unless you are talking about 42.8 x10 - 6= 428- 6= 422, that "-6" certainly is an exponent!

As Andrevdh said,
$$(3.652 \times 10^8)(42.8 \times 10^{-6})=15630.56$$
Since 42.8 x 10^-6 has 3 significant figures, that would be written as 15600 or, better, 1.56 x 10⁴.

 

[Mozart]

Now I am not sure if it is an exponent or not because the teacher wrote it out exactly like this on the paper she distributed. (42.8 x 10-6)

I don't know why she would do that. She usually always has it as a superscript, and this is just smack in the middle.

In another question I noticed that she wrote something like (6.32 x 102 - 15.73) There is a space between each side of te negative sign. Is it a mathematical convention or something to recognize say 42.3 x 10-3 in which the 3 is an exponent unless spaces are put between the - sign?

 

[nrqed]

Now I am not sure if it is an exponent or not because the teacher wrote it out exactly like this on the paper she distributed. (42.8 x 10-6)

I don't know why she would do that. She usually always has it as a superscript, and this is just smack in the middle.

I *think* that she meant it as an exponent. Normally, one writes powers of 10 as a superscript, you are right. But as a teacher myself, I have sometimes resorted to writing shorthand expressions in my typed assignments because it is a pain in the neck to enter equations in Word. But I personally would write 42.8 x 10^-6 to indicate that it's an exponent. But I have seen people writing 10-6 simply (others write E-6). However, it is rare that people write numbers with two digits before the decimal point when using scientific notation, i.e. people would usually write 4.28 x 10^-5, but it is just a convention.

So my bet would be that she meant a power of 10. In that case that number has 3 sig figs.

In another question I noticed that she wrote something like (6.32 x 102 - 15.73) There is a space between each side of te negative sign. Is it a mathematical convention or something to recognize say 42.3 x 10-3 in which the 3 is an exponent unless spaces are put between the - sign?

No, she probably meant there (6.32 x 102) - 15.73... No exponent!

The rule is that *usually*, when you see 10 followed by minus or plus a number (with one or two digits), it means scientific notation.

Hope this helps

Pat

 

[Mozart]

Yup I'm convinced its an exponent now. Thanks for clearing this up guys.

 

[andrevdh]

It is best to clear it up with your teacher - make her aware of the problem, and possibly retrain her by reminding her ever now and then of the ambiguity. have sympathy for the situation though since us humans do not have the capabilities of modern day technology in this respect. If I could make a suggestion, maybe a convention should be introduced in order to avoid this confusion when us humans write by hand for e.g. $3.30 \times 10^6$ shoud be written as
$$3.30 \times 10\ \bar 6$$
for superscript parts of a numerical value and $\hat v$ for vectors.