Question #50f95

1 Answer
Jun 10, 2015

Unit conversions with scientific notation are all about base 10 exponents.


I'll show you how to do a couple of conversions using scientific notation and then redirect you to some videos.

When you're doing unit conversion with scientific notation, you have to keep track of the base 10 exponents. If you're converting between two SI units, the base 10 exponents will be the only ones that change.

Until you get used to the multiplication factors that get you from one unit to another, use a metric conversion chart.

So, in your case, you have #1.78*10^(6)"g"#. Let's say that you want to convert this value to kilograms. The chart tells you that you need a multiplication factor of #10^3# to get from the unit, in your case grams, to the kilo unit, in your ase kilograms.

This means that you need 1000 g to make a kg, or, in other words, that 1 kg contains #10^(3)# **grams. You would write

#1.78 * 10^(6)cancel("g") * "1 kg"/(10^(3)cancel("g")) = (1.78 * 10^cancel(6))/cancel(10^(3)) = 1.78 * 10^(3)"kg"#

Notice that you only had to work with the base 10 exponents.

Now let's say that you want to convert this value to micrograms. The multiplication factor is equal to #10^(-6)#, which means that you need #10^(6)# micrograms to get 1 gram.

You would write

#1.78 * 10^(6)cancel("g") * (10^(6)mu"g")/(1cancel("g")) = 1.78 * 10^(6 + 6) = 1.78 * 10^(12)mu"g"#

Now let's say that you want to convert to gigagrams. The multiplication factor is equal to #10^9#, so you need #10^9# grams to get to 1 gigagram. You would write

#1.78*10^6cancel("g") * "1 Gg"/(10^(9)cancel("g")) = (1.78 * cancel(10^(6)))/10^(cancel(9)) = 1.78/10^3 = 1.78 * 10^(-3)"Gg"#

Now, let's say that you want to convert to ounces. The conversion factor between these two units has 1 ounce equal to 28.3495231 grams. This time, the base 10 exponent is not the only one that changes. You would write

#1.78*color(blue)(10^(6))cancel("g") * "1 ounce"/(28.3495231cancel("g")) = 0.0628 * color(blue)(10^(6)) = 6.28 * 10^(4)"ounces"#

Two things to notice here

  • You divide the regular numbers first, and leave the base 10 number unchanged;
  • Then you use the base 10 number to express the result in scientific notation.

You can check out the videos available on Socratic:

Other videos: