Issue with exponents in inductance

[Mati256]

Hello. I'm studding for an exam and I came across this exorcise, after I did it I check the answer to find that my maths are wrong.
Am I or is the exorcise wrong?
10⁴ x 500x10^-6 = 50 Ohms right? 

[Andy Watson]

Careful how you push the buttons on your calculator. 10^4 is 10000, not 10 exp 4 (which a calculator will treat as 10 x 10^4).

[Mati256]

You are rihgt! 
Thank you!

[IanB]

This is why engineers should practice doing estimates on paper or by mental arithmetic and not rely too much on button pushing.

From high school maths:

  10⁴ x 500x10^-6
    = 500 x 10⁶ x 10^-4
    = 500 x 10^(6-4)
    = 500 x 10^-2
    = 500 / 100
    = 5

[Refrigerator]

This is why engineers should practice doing estimates on paper or by mental arithmetic and not rely too much on button pushing.

From high school maths:

  10⁴ x 500x10^-6
    = 500 x 10⁶ x 10^-4
    = 500 x 10^(6-4)
    = 500 x 10^-2
    = 500 / 100
    = 5

That's pretty much exactly the same math they were teaching in my school last week, incredibly easy and boring, you don't even need a calculator to solve these kind of equations.

[Timmay]

This is why engineers should practice doing estimates on paper or by mental arithmetic and not rely too much on button pushing.

From high school maths:

  10⁴ x 500x10^-6
    = 500 x 10⁶ x 10^-4
    = 500 x 10^(6-4)
    = 500 x 10^-2
    = 500 / 100
    = 5

True but as I put this in my TI, mathway, matlab, excel, wolfram and my cellphone I got the correct answer. So as much as you should easily should be doing this by hand, you should equally know how to do it on a calculator or equivalent program. If you make mistakes often, then it shows you don't quite understand the concepts behind the math and that can be a problem. We all make mistakes, but calculators are key to anyone in any STEM field.

[IanB]

It's not a question of doing it by hand instead of doing it on a calculator, it is a question of knowing how to estimate whether the answer you got out of the calculator is in the right ballpark, just in case you made a button pressing error. So for example, you should know how to tell by eye whether the answer should be about 0.5 ohms, 5 ohms or 50 ohms, even if the exact answer happens to be 57.3 ohms.

[VK5RC]

This was where slide rules taught you a lot.  You always did an order of magnitude calculation in your head.

[Timmay]

It's not a question of doing it by hand instead of doing it on a calculator, it is a question of knowing how to estimate whether the answer you got out of the calculator is in the right ballpark, just in case you made a button pressing error. So for example, you should know how to tell by eye whether the answer should be about 0.5 ohms, 5 ohms or 50 ohms, even if the exact answer happens to be 57.3 ohms.

I concede, very true. I will add that confidence in both your written and calculated answers is important and that with time, learning enough of the concepts behind it all will lead you to the point IanB makes. Maybe take an approach my school did: Calculated, Simulated and Physical. With math you do the problems and find your answers, then simulate them with some decently cheap software like Multisim and if time permits use a breadboard approach to go into it more. However, as I agree with IanB knowing all the angels of a problem, doing them more and more often will get you to the point IanB makes.