Question

Which of the following is a possible equivalence that can be used in a conversion?

ten cubed kL over one L

ten squared daL over one L

ten to the negative second power L over one cL

ten to the negative first power L over one mL

Answer 1

The answer is the third one. :)
Firstly, when you convert to a different unit, the value - what the number represents - doesn't change. You're actually multiplying the number by 1. Its a fraction, where the top and bottom are equal. I'll derive a simple conversion that I hope you agree with.

Even if you're in the stubborn U.S., it's important to know the metric system. Like, 1 meter is one hundred centimters. In math, 1 [m]=100 [cm]
This would imply that, by dividing by 1 meter,
1 [m]1 [m]=100 [cm]1 [m]
⇓
1 [m]1 [m]=100 [cm]1 [m]
⇓
1=100 [cm]1 [m]

That sort of thing is always good to know for unit conversions. And reversing that on your multiple choices will check to see if they are good!


103 [kL][L]→103 [kL]=?[L]


102 [daL][L]→102 [daL]=?[L]

10−2 [L][cL]→10−2 [L]=?[cL]

10−1 [L][mL]→10−1 [L]=?[mL]


And note that 10−1=1101 and that 10−2=1102, just by the meaning of negative exponents. Just for my own fun...


103 [kL][L]→103 [kL]=[L]


102 [daL][L]→102 [daL]=[L]

10−2 [L][cL]→10−2 [L]=[cL]✓

10−1 [L][mL]→10−1 [L]=[mL]