2
$\begingroup$

How do i solve this using Scientific Notation? $$ \frac{3\times 10^8}{4\times 10^{-5}} $$
I have been trying for hours now! Help please

$\endgroup$
4
  • 4
    $\begingroup$ What is $3\div4$? What is $10^8\div10^{-5}$? $\endgroup$ – peterwhy Nov 11 '14 at 16:07
  • $\begingroup$ If you've been trying for hours, the calculator might be of some use. I know that's usually not how we want to approach math but I think that it makes more sense to try that first than to post a question. $\endgroup$ – inkievoyd Nov 11 '14 at 16:07
  • $\begingroup$ Scientific notation is significant figures I.e $0.01 = 1.00\times 10^{-2}$ to 3 significant figures. Does this help? $\endgroup$ – Chinny84 Nov 11 '14 at 16:12
  • $\begingroup$ but for 10⁸÷10−⁵ do i only divide the indices? or all of it? $\endgroup$ – GeoGod Nov 11 '14 at 16:13
1
$\begingroup$

$$\dfrac {a^c}{a^d} = a^{c-d}$$

So your fraction is $$\frac{3\times 10^8}{4\times 10^{-5}} = \dfrac 34\times 10^{8 - (-5)} = \dfrac 34 \times 10^{13} = 0.75\times 10^{13}= 7.50 \times 10^{12}$$

$\endgroup$
1
$\begingroup$

First note that $$ \frac{x^a}{x^{-b}}= \frac{x^a}{\frac{1}{x^{b}}}=x^ax^b =x^{a+b}, \quad x\not =0$$ So now $$ \frac{3\times 10^8}{4\times 10^{-5}}= \frac{3}{4}\times \frac{10^8}{10^{-5}}= \frac{3}{4}\times 10^8\times 10^5 $$ $$= 0.75\times 10^{8+5}= 0.75\times 10^{13}=7.5\times 10^{12}$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.