such as kilo to centi
first a brief introduction to what metric prefixes are,
and then onward to converting...
we will work from a horizontal chart
showing the name of each prefix,
the symbol for each prefix,
and the exponent of 10 that the prefix represents.
and note that this chart is available via the link in the description below.
so all prefixes are used with a base unit such as gram, meter, or liter, and there are many other base units.
all prefixes are used with a base unit,
and since each prefix represents a number it is a shorthand for representing a specific amount of that base unit.
for example in one kilogram, kilo is the prefix and gram is the base
it can be abbreviated with their symbols: kg for kilogram, and its meaning comes from the exponent
kilo is 10^3 so kilogram is 10^3 grams or 1000 grams
let's try centimeter with centi as prefix
meter as base
its abbreviation is cm which represents 10^-2 meters or 0.01 meters
lastly it is very important to note
that any number can be expressed using prefixes
putting an 8 in front of milliliter gives us
8 milliliters or 8 mL
which represents...
now let's get to converting from one prefix to another
the chart is laid out in this manner specifically to give easier access to the exponent represented by each prefix
note that the base unit is just 1, or 10^0
our first example is converting 0.150 meters to centimeters
note that when a symbol is by itself it is always a base unit, in this case meter
the conversion follows two simple rules first is to subtract exponents
so we have meter, and we want to get to centi with an
with an exponent of zero
and we want to get to centi
with an exponent of -2
write down the exponents and subtract,
giving a difference of two [ 0 - (-2) = 2 ]
beginning with 0.150, the decimal is moved two places to the right
giving 15.0 centimeters
we have moved the decimal two places to the right.
next problem,
0.150 kilometers is equal to how many centimeters?
using the same two steps we see that we are
starting with kilo and want to get to centi,
exponent for kilo is 3 and
and for centi is -2, we subtract and
3 - (-2) = 5
the wanted unit
0.150 moving the decimal five places to the right,
note there are now blank spaces
always fill in the blanks with zeros
so we now have 15,000.
for the first two examples
we went from a larger unit to a smaller unit
let's see how to convert from a
smaller unit to a larger unit.
384.0 milligrams is how many decigrams
we use the same steps as before
we are starting with milli and want to get to deci
the exponent for milli is -3 and for deci it is -1
we subtract, (-1) - (-3) = 2
deci is the wanted unit
starting with 384.0 the decimal is moved
two places to the left, which gives
let's try one more problem
stop the video see if you can work out problem #4
and then start the video to check your answer.
notice that the first symbol is by itself
so it is a base unit.
so we want to start with the base unit LITER
and want to get to mega.
base units have an exponent of 0, mega is 6
the decimal is moved six places to the left
blanks are filled with zeros, by convention we add zero before the decimal.
all you need is this chart and the two rules
if you want the chart it is linked in the description below