# orders of magnitude

• Mar 25th 2009, 05:35 PM
xcelxp
orders of magnitude
This question is not for a homework assignment.. It's just something that has really been bugging me

If I was to decrease the number 125,278,840 by two orders of magnitude

would I simply divide it by 100?

I've read somewhere that in order to increase a number by two orders of magnitude you multiply by 100

Thanks for your help!
• Mar 25th 2009, 05:53 PM
Reckoner
Quote:

Originally Posted by xcelxp
If I was to decrease the number 125,278,840 by two orders of magnitude

would I simply divide it by 100?

Yes, assuming you are scaling by 10. In general, to increase a number by $n$ orders of magnitude, multiply by $10^n.$ In this case we have $10^{-2}=\frac1{100}.$

Why does this make sense? The order of magnitude of a number is basically the largest power of ten that is less than the number. $125\,278\,840$ is on the order of $10^8$ (its order of magnitude is 8), and to decrease it by two orders of magnitude would make it on the order of $10^6.$ Dividing by $10^2=100$ accomplishes this.