# Question aa655

Oct 11, 2016

Here's how you can do that.

#### Explanation:

The units given to use are expressed using metric prefixes, which as you know are based on the powers of $10$.

color(blue)(ul(color(black)("going from"color(white)(a)mu"g to g or vice versa"))

The prefix micro is used to denote a fraction of a given unit. In this case, a microgram is simply a fraction of a gram, i.e. you can get from micrograms to grams by dividing by a number.

More specifically, a microgram is the ${10}^{6} \text{th}$ part of a gram.

$\textcolor{p u r p \le}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 g" = 10^6mu"g}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that

• you get from micrograms to grams by dividing by ${10}^{6}$
• you get from grams to micrograms by multiplying by ${10}^{6}$

So micro simply means that you must divide by ${10}^{6}$ to get to the base unit.

color(blue)(ul(color(black)("going from kL to cL or vice versa"))

Here the prefix kilo is used to denote a multiple of a base unit and the prefix centi is used to denote a fraction of a unit.

More specifically, you get from kiloliters to liters by multiplying by ${10}^{3}$ and from centiliters to liters by dividing by ${10}^{2}$.

color(purple)(bar(ul(|color(white)(a/a)color(black)("1 kL" = 10^3"L")color(white)(a/a)|)))" " and " "color(purple)(bar(ul(|color(white)(a/a)color(black)("1 L" = 10^2"cL")color(white)(a/a)|)))

This means that you can use the liter to find a direct conversion factor between kiloliters and centiliters

1 color(red)(cancel(color(black)("kL"))) * (10^3color(red)(cancel(color(black)("L"))))/(1color(red)(cancel(color(black)("kL")))) * (10^2"cL")/(1color(red)(cancel(color(black)("L")))) = 10^5"cL"

This means that

• you get from centiliters to kiloliters by dividing by ${10}^{5}$
• you get from kiloliters to centiliters by multiplying by ${10}^{5}$

color(blue)(ul(color(black)("going from nm to mm or vice versa"))

This time, you're dealing with two prefixes that are used to denote fractions of a base unit.

You can go from millimeters to meters by dividing by ${10}^{3}$ and from nanomenters to meters by dividing by ${10}^{9}$

color(purple)(bar(ul(|color(white)(a/a)color(black)("1 m" = 10^3"mm")color(white)(a/a)|)))" " and " "color(purple)(bar(ul(|color(white)(a/a)color(black)("1 m" = 10^9"nm")color(white)(a/a)|)))

A direct conversion factor between millimeters and nanometers would look like this

1 color(red)(cancel(color(black)("mm"))) * (1 color(red)(cancel(color(black)("m"))))/(10^3color(red)(cancel(color(black)("mm")))) * (10^9"nm")/(1color(red)(cancel(color(black)("m")))) = 10^(6)"nm"#

This means that

• you get from nanometers to millimeters by dividing by ${10}^{6}$
• you get from millimeters to nanometers by multiplying by ${10}^{6}$