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I'm taking a practice test on scientific notation. The question is What is .000563x10-7 in proper scientific notation. I chose the answer 5.63x10-3. However, this answer was incorrect and I'm not sure why. Does anyone know what the proper answer would be?

Thanks, Dave

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  • $\begingroup$ The $5.63$ part is right. But what most likely happened is that you messed you your calculations. When you move the decimal point to the right $4$ times, you "add" to the exponent to obtain the answer by heather. $\endgroup$ – Frank Oct 2 '16 at 18:17
  • $\begingroup$ You can think of it like his too $.000563\times10^{-7}=\frac{5.63}{1000}\times10^{-7}$. At which point you can divide the times ten part to reduce the exponent $\endgroup$ – Triatticus Oct 2 '16 at 18:21
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Tedious but important to get the concept way:

$.000563\times 10^{-7} = .000563 \times 0.0000001 = .0000000000563 =$ (count the decimals) = $5.63 \times 10^{-11}$

More straight forward after you've gotten the concept.

$.000563 \times 10^{-7} = 5.63 \times 10^n \times 10^{-7} = $ (count the decimals) $ 5.63 \times 10^{-4} \times 10^{-7} = 5.63 \times 10^{-11}$.

So what did you do wrong? You added the 4 rather than subtracted the for. Thing is $10^{-7}$ means make smaller means shift decimal point further to the left-- if the decimal is already to the left shift it further.

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  • $\begingroup$ Thanks everyone. This makes sense now! Dave $\endgroup$ – Dave Oct 3 '16 at 0:27
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I believe it'd be $5.63\times 10^{-11}$.

You messed up your exponents. It'd be $\times 10^{-11}$ because it is already at 7 and you add 4 more movements (to the right) of the decimal point. Real quick I'll go through it step by step. You started with $0.000563\times 10^{-7}$. Then, you pick a number between $1$ and $10$ from that sequence of digits, in this case $5.63$. Then, count the number of spaces you'd have to move the decimal point to the right or left to get that number (where moving it to the right is negative), in this case $-4$. Then, add that to the current exponent, in this case $-7$, for the end result of $-11$. This then gives $5.63\times 10^{-11}$.

Hope this helps!

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