In this energy conservation problem, why are the answers different with different units? [closed]

Really basic question, but basically I'm given a change in height in centimeters (that's how I measured it). From that, I'm supposed to find the initial kinetic energy.

$KE_i = PE_f$

After doing some work, the masses cancel out and I'm left with:

$v_i=\sqrt{2g\bigtriangleup h}$

So my change in height is 8.80 cm. If I input that, my velocity turns out to be 13.1 cm/s. However, if I initially convert it to meters, it ends up being 1.31 m/s. 13.1 centimeters definitely isn't the same as 1.31 meters.

I can see that the square root is the problem, but why? And what should I actually do?

In addition, if there is a square root in kinematic equations as well, does it need to be in meters or something?

closed as off-topic by Bill N, user36790, CuriousOne, AccidentalFourierTransform, Qmechanic♦May 5 '16 at 10:18

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• Check your units again, very carefully. What value of $g$ did you use to get 13.1 cm/s? – tpg2114 May 5 '16 at 2:55
• If you are using cm for the change in height what units are you using for g? They should be 980 cm/s/s if you want to get speed in cm/s. – M. Enns May 5 '16 at 2:56
• Did you use 980 cm/s^2 for g? Always check for consistent units! – Bill N May 5 '16 at 2:56
• I'm voting to close this question as off-topic because the OP didn't check for proper units. – Bill N May 5 '16 at 2:57

I think your problem is that you didn't change the units in the constant g. It has a value of approximately $9.8ms^{-2}$. Notice that it depends on meters. To obtain the correct result, you should use $980cms^{-2}$. Notice that this constant is off by a factor of 100, so that the result (after the square root) is off by a factor of $\sqrt{100}=10$.