Hey quick basic question. Preface: I have been drinking a small bit (two regular beers over 2 hours) so I may be missing something here but I am pretty sure I'm not.

When something asks you to rank a series of numbers in scientific notation by magnitude, and not in least to greatest order, an exponent of -6 magnitude would be greater than an exponent of +3 magnitude right?

It was my understanding throughout my mathematical career that magnitude takes into account the number, regardless of positivity or negativity. I was told through our 'infallible' (very, very fallible. our professor corrects something weekly) online homework service that I got the following question wrong:

Rank these values according to magnitude: 2.1×10^5, 5.9 × 10^4, 4.5×10^-2, 9.0×10^-6, 8.1×10^-6

I ranked them (ignoring exponents to save time) 9.0, 8.1, 2.1, 5.9, 4.5

To my understanding, I did that correctly, and magnitude is magnitude and not 'from greatest to least'. Just want to make sure before I send off an email.

When something asks you to rank a series of numbers in scientific notation by magnitude, and not in least to greatest order, an exponent of -6 magnitude would be greater than an exponent of +3 magnitude right?

It was my understanding throughout my mathematical career that magnitude takes into account the number, regardless of positivity or negativity. I was told through our 'infallible' (very, very fallible. our professor corrects something weekly) online homework service that I got the following question wrong:

Rank these values according to magnitude: 2.1×10^5, 5.9 × 10^4, 4.5×10^-2, 9.0×10^-6, 8.1×10^-6

I ranked them (ignoring exponents to save time) 9.0, 8.1, 2.1, 5.9, 4.5

To my understanding, I did that correctly, and magnitude is magnitude and not 'from greatest to least'. Just want to make sure before I send off an email.