scientific notation

[imadummy]

Please tell me plugging answers is the best way...


If (0.0015*10^m)/(0.03*10^k) = 5*10^7 then m-k=?

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[VP_RedSoxFan]

I'd just convert the decimal places in the numerator and denominator until I had something I didn't think I could make a careless error in the division on.

(15*10^-4*10^m)/(3*10^-2*10^k) = 5*10-2*10^(m-k) = 5*10^(m-k-2)

Since 5*10^(m-k-2) = 5*10^7, we know that m-k-2=7 and that m-k=9

Answer choice [A]

[lunarpower]

Please tell me plugging answers is the best way...


If (0.0015*10^m)/(0.03*10^k) = 5*10^7 then m-k=?

9
8
7
6
5

plugging answers is the best way. there, i followed your instructions.

actually, in this problem, plugging answers may well be the best method of solution. you can pick one of the answer choices, and then pick an arbitrary 'm' and 'k' that give the correct difference; plugging that 'm' and 'k' into the equation should yield 5 x 10^7. this works admirably here.

HOWEVER,

that's not the case on all problems like this. you see, there are two distinct possibilities for a problem that looks like this, with numerical answer choices listed for the difference (m - k):
1) ANY 'm' and 'k' with the proper difference will work;
2) there are actually specific values that can be found for 'm' and 'k', and the problem is just asking for the difference to be annoying (= to thwart the plug-in-answers strategy).
this problem happens to fall into category (1), so you're lucky, and plug-in-answer-choices will work.

--

what i really think is the best way to solve this problem is to use your knowledge of exponents to recognize right away that the exponents 'm' and 'k' are going to be subtracted, and to proceed accordingly (as is done in the post above). the reason i think that's the best way is that it will work on all problems that look like this one.

[rbales]

I don't get the last few steps. The OG text shows the last steps as follows:

=> 10^(m-4-(k-2)) = 10^7
=> m - 4 - (k-2) = 7
=> m - k - 2 = 7
=> m - k = 9

so... what happened to the 4 after step 2?

[neelgandham]

I don't get the last few steps. The OG text shows the last steps as follows:

=> 10^(m-4-(k-2)) = 10^7
=> m - 4 - (k-2) = 7
=> m - 4 -k + 2 = 7
=> m - k -4 + 2 = 7
=> m - k +(2-4) = 7
=> m - k +(-2) = 7
=> m - k - 2 = 7
=> m - k = 9

so... what happened to the 4 after step 2?

Please find the answer to your question above in Red !