Conversions of Units, Estimates, and Order of Magnitude Calculations: The Physics Lecture Series Chapter 1 Sections 4 and 5.

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is focusing on conversion of units that you'll see in Physics, Chemistry, Biology, and all of science.

Unit Conversion

The previous Physics section allows us a mechanism to convert from one unit to another unit of the same type.  To do this, we take advantage of the equivalence between two values, and multiply with what is effectively equivalent to one.  For example, notice that 1hr=60min.  If we divide both sides by 1hr, we get $\frac{1hr}{1hr}=\frac{60min}{1hr}$.  In all of science, units such as seconds, meters, and kilograms can be canceled if in a quotient or squared if multiplied together, much like variables.  With that in mind, notice that on the left hand side, the hours cancel and the ones cancel, so that we have $1=\frac{60min}{hr.}, which makes sense since there are 60 minutes per hour.  This general concept applies to all conversion factors.  Multiplying by a conversion factor (the form of the fraction) is equivalent to multiplying by 1, so it's always valid to perform this operation.  This will always go from one unit to another.

Estimates and Order of Magnitude Calculations

An order of magnitude is a power of ten, so 100 is an order of magnitude (one power of ten) larger than 10.  In order to estimate an order of magnitude of a multiplication or division, follow these steps:
  1. Convert to scientific notation.
  2. If the result is less than $\sqrt{10} \times 10^{n}, then the order of magnitude is n.  Otherwise, it's n+1.
That's the end of this section.  If you have any questions, please leave them is the comments.  Like and share this post if you found it helpful.  And until next time, stay curious.

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