Convert the exponents in the following to the convenient prefixes of the units so that the number is between 1 and 1000 followed by a prefix and unit.

I have done a) 3x10^5m
| |
3x10^2 10^3k
=300 km
But I don't know what to do if it's a negative, for example
b) 7x10^-7s

Convert the exponents in the following to the convenient prefixes of the units so that the number is between 1 and 1000 followed by a prefix and unit.

I have done a) 3x10^5m
| |
3x10^2 10^3k
=300 km

Looks good.



But I don't know what to do if its a negative, for example
b) 7x10^-7s

The negative exponent means that the uint is in "Thousandths" or "millionths" or whatever. For example, 10^-3 means one one thousandth, so for example 7x10^-2 m = 70x10^-3m = 70 thousandths of a meter, or 70 mm. For your problem of 7x10-7s you should convert to something times ten to the minus 9, because that puts it in units of billionths of a second, otherwise known as picoseconds. Post back and let us know what you get.

The thing is that I could do the same thing as I did for the first one but that would be:

7x10^-1... 10^-6micro
=0.7 micro seconds
but the answer should be between 1 and 1000 so I was thinking I am supposed to convert that to milli but I don't know if that would be right.

PS. To the -9 is nano, pico is to the -12 :)

The thing is that I could do the same thing as i did for the first one but that would be:

7x10^-1.......10^-6micro
=0.7 micro seconds
but the answer should be between 1 and 1000 so I was thinking I am supposed to convert that to milli but i dont know if that would be right.

PS. to the -9 is nano, pico is to the -12 :)

Ah - yes, "nanoseconds" is indeed 10^-9 seconds - good catch!

Seems to me you are just about at the answer. You don't want it to put it into milliseconds, as that would make the answer 0.0007 miliseconds, but rather put it in terms of a smaller division of time - like nanseconds. You know that 1 microsecond equals 1000 nanseconds; so, 0.7 microseconds equals how many nanoseconds?

I have actually figured it out last night, don't know if I'm right but:

7x10^2... 10^-9 n
= 700 ns

If u check it backwards its right but I don't know if I am allowed to solve it like that

Right. You can check your work thusly:

700 nanseconds = 700* 10 -9 sec = 7 * 10^2 * 10-9 = 7 * 10^-7 sec.

You could have gotten the answer this way:

Realizing you want to find a power of 10 that is divisible by three and that is smaller than the number you are working with, you can see that 10^9 is the next smallest unit that fits this criteria. This means you need to find a solution to:

7*10^-7 = X*10^-9
So X = 7*10^-7/10^-9 = 700.

Hence 7*10^-7 = 700 * 10-9 = 700 nanseconds.

So I guess I can solve it that way.

Thank you for all your help!! :)