# Question #aa655

##### 1 Answer

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*

#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

#color(purple)(bar(ul(|color(white)(a/a)color(black)("1 g" = 10^6mu"g")color(white)(a/a)|)))#

This means that

you get frommicrogramstogramsby dividing by#10^6# you get fromgramstomicrogramsby multiplying by#10^6#

So *micro* simply means that you must **divide** by

#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 *centiliters* to *liters* by **dividing** by

#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 fromcentiliterstokilolitersby dividing by#10^5# you get fromkiloliterstocentilitersby 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 *nanomenters* to *meters* by **dividing** by

#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#