Find Magnitude of Order: What is it?

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The discussion clarifies the concept of "magnitude of order," explaining that it refers to the exponent in scientific notation, which indicates the order of magnitude. Examples like 9.10645x10^5 and 6.5x10^-5 illustrate how numbers can be categorized by their powers of ten. It is noted that numbers such as 1,253,000 and 7,552,215, while different, fall within the same order of magnitude, which is millions or 10^6. Participants express surprise that this concept wasn't covered in their lessons. Understanding the order of magnitude simplifies comparing large numbers effectively.
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What is meant by "find the magnitude of order?" What is it? The Qs on my homework are numbers such as 9.10645x10^5 and 6.5x10^-5.
 
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The "order of magnitude" to the power of 10.
 
The exponent is the order of magnitude?
 
Well yes, more or less.

For example, 1.253.000 and 7.552.215 aren't the same but they're in the same order of magnitude, being millions here. You could say that the order here is "6", since they can be written as x,y * 10^6
 
Ok thanks, that's easy. I don't know why my teacher didn't teach us that!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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