Unit conversions step by step procedure



Unit conversions step by step procedureHere is a step by step procedure for how to do the conversions. I will include the conversion tables from the book and the lab for the exam, but I will not be including this set of instructions. Start by identifying the units you haveWhat are you starting with? What was your measurement or, what were you given in the problem as the starting value?Identify which units the problem is asking forWhat are the units that are indicated in the blank answer or what are the standard units for the final answer (this would be indicated in the exam).Look up conversion factors that will link the units you have with the units you want (for the exam I will include the chart from the lab protocol AND the one from the book, so be sure you can use at least one of them correctly!!!!)Often you will not have a single conversion factor that will link your starting value units with your final answer units. In this case you will use several conversion factors which share an intermediate unit to link them. For example, if you are starting with mm and ending with km, you will use 2 conversion factors: 1) 1km=1000m and .001m = 1mm. They are linked by the standard unit of meters (m) which serves as an intermediate unit for this problem. Sometimes you will need to square or cube a conversion factor. If you start with cm2 and need to end with mm2 then you need to square the conversion factor that you know or which can be looked up. Create the conversion factor that you need through the conversion factors you can look up such as .01m = 1cm and .001m = 1mm, then you multiply everything to get .1cm = 1mm. Next, you square both sides to get .001cm2 =1mm2You can then use this conversion factor in your problem. Alternatively you don’t have to do everything separate, you can do the squaring as part of the entire conversion process in one step, but if that confuses you, stick to creating the conversion factor first. For any conversion factor, a fraction of the two values is always equal to one To understand this, if you divide both sides of the equation by one of the values in the conversion factor you end up with a fraction that equals one. For example, if you divide the conversion factor 1km=1000m by 1km you end up with 1km/1km=1000m/1km which is equivalent to 1=1000m/1km. However, if you divided by 1000m instead you would end up with 1km/1000m=1. Both 1km/1000m and 1000m/1km are equal to each other and both are equal to 1. Thus whenever you multiply by a conversion factor, you are always just multiplying by 1, which doesn’t change the equation. Convert all values into scientific notation If you move the decimal to the left this will increase the base 10 by 1 for example going from 101 to 102 or 100 to 101. If you move the decimal to the right this will decrease the base 10 by 1 for example going from 102 to 101 or 100 to 10-1. When the exponent to the base 10 is less than zero, this means that it is a number smaller than 1. In other words it is the same as dividing by the base 10 with a non negative number. So 1x10-1 is the same as 1/(1x101). This is also equivalent to 1/10 which is equivalent to 0.1For values where the decimal does not need to be moved use 100 as the base 10 value(anything to the power of zero always equals one). For example, 2.45cm becomes 2.45 x 100cm, both forms represent the same number. Set up an equation with all of your conversion factors. This is often the trickiest part, but if you do everything in a particular order without skipping steps, you can keep from confusing yourself. Remember the goal is to have all units cancel out except the final units you desire. I usually start with a linking conversion factor that contains the final units and make sure those units are on the same side (top or bottom, aka numerator or denominator) as those that are needed for the final answer. Then I set up the next linking conversion factor if needed to cancel out the intermediate units (such as meters in the procedure 3b above). I repeat this process until I end up with units that will cancel out the starting units. If your starting units don’t cancel out and they are different then the final units, then you have done something wrong. After canceling all of the units do the arithmetic in the appropriate orderProcess the insides of parentheses or brackets prior to using any of those values in subsequent operations such as multiplication and addition. For example (4+3)*5 is first computed 4+3=7, then multiply by 5; 7*5=35. Doing it in the wrong order gives you an incorrect answer 3*5=15; then 15+4=19. 19 is the wrong answer. Always start by computing the exponents if there are anyThen compute any values that are multiplied or dividedThen compute any values that are added. See the handout for how to handle base 10 values when multiplying or adding scientific notation. Put your final answer in scientific notation, unless the problem indicates otherwise. If there are two different units (such as for density), you can do: a) one unit first and then do the other unit after or b) do them both at the same time with more conversion factors between the starting value and the ending value, but only multiplying the top and bottom only once. So for example, if you measured something as 5mg and a volume of 12mm3, and you are to report the final answer in g/cm3. There are several steps you must perform.Convert mg to gConvert mm3 to cm3 and this will require:Creating a conversion factor from two conversion factors each with an intermediate unit of meters. Cubing the conversion factor computed from aboveUsing this conversion factor to cancel out mm3 to give cm3For more see online videos, there are many different sources, Khan academy, youtube, etc. For khan academy, they have several different videos in different sections which cover the same material of unit conversions, but here is one that you might find useful: you are interested in other videos at Khan academy just search for either unit conversion, metric conversions, scientific notation, etc. ................
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