Examples of eqivalent amounts include:
0.5 kg = 500 g 0.25 g = 250 mg 0.2 mg = 200 mcg 0.5 L = 500 mL 0.25 mol = 250 mmol
CONVERSION FROM ONE UNIT TO ANOTHER
In drug calculations, it is best to work in whole numbers, i.e.
125 micrograms rather than 0.125 mg, as fewer mistakes are then made.
Avoid using decimals, as the decimal point can be written in the wrong place during calculations. A decimal point in the wrong place can mean 10-fold or even 100-fold errors.
It is always best to work with the smaller unit in order to avoid decimals and decimal points, so you need to be able to convert easily from one unit to another. In general:
• To convert from a larger unit to a smaller unit, multiply by multiples of 1,000.
• To convert from a smaller unit to a larger unit, divide by multiples of 1,000.
For each multiplication or division by 1,000, the decimal point moves three places, either to the right or left depending upon whether you are converting from a larger unit to a smaller unit or vice versa.
There are two methods for converting units: moving the decimal point or by using boxes which is an easy way to multiply or divide by a thousand (see the worked examples below).
When you have to convert from a very large unit to a much smaller unit (or vice versa), you may find it easier to do the conversion in several steps.
For example, to convert 0.005 kg to milligrams, first convert to grams:
0.005 kg = (0.005 × 1,000) g = 5 g Next, convert grams to milligrams:
5 g = (5 × 1,000) mg = 5,000 mg
WORKED EXAMPLE Convert 0.5 g to milligrams.
METHOD ONE:MOVING THE DECIMAL POINT
You are going from a larger unit to a smaller unit, so you have to multiply by 1,000, i.e.
0.5 × 1,000 = 500 milligrams The decimal point moves three places to the right:
0 . 5 0 0 = 500
METHOD TWO:USING BOXES
Place the higher unit in the left-hand box and the smaller unit in the right-hand box:
g mg
When you do conversions like this, the amount remains the same: it is only the units that change. Obviously, it appears more when expressed as a smaller unit, but the amount remains the same. (200 pence is the same as £2, although it may look more.)
REMEMBER
Conversion from one unit to another 65
Next place an arrow between the units pointing from the unit you are converting from towards the unit you are going to. In this example, we are converting from grams (g) to milligrams (mg), so the arrow will point from left to right:
Next enter the numbers into the boxes, starting from the column of the unit you are converting from, i.e. in this example, it will be the left-handside. Enter the numbers 0 and 5 (0.5 kg):
Place zeros in any empty boxes
Now we have to decide where to place the decimal point.
Remember, when converting units you either multiply or divide by 1,000 (or multiples thereof). The decimal point moves three places to the left or the right. The arrow indicates which way the decimal point moves. In this case, it is pointing to the right, so starting at the right of the original place of the decimal point, add the numbers 1, 2 and 3 in the boxes:
The decimal point is then placed to the right of the 3, giving an answer of 500. Add the new unit, mg, to get a final answer:
So the answer is 500 milligrams.
g mg
0 5
1 0 2
0 .
3
g mg
g mg
0 5
1 0 2
0 3
g mg
0 5 0 0
g mg
0 5
WORKED EXAMPLE Convert 2,000 g to kilograms.
METHOD ONE:MOVING THE DECIMAL POINT
You are going from a smaller unit to a larger unit, so you have to divide by 1,000, i.e.
2,000 g =
( )
kg = 2 kgThe decimal point moves three places to the left:
2 0 0 0 . = 2 kg
METHOD TWO:USING BOXES
Place the higher unit in the left-hand box and the smaller unit in the right-handbox:
Next place an arrow between the units pointing from the unit you are converting from towards the unit you are going to. In this example, we are converting from grams (g) to kilograms (kg), so the arrow will point from right to left:
Next enter the numbers into the boxes as seen, starting from the unit you are converting from, i.e. in this example from the right-hand side:
So, the numbers are written 0, 0, 0 and 2 to give 2,000 g:
Now we have to decide where to place the decimal point. We are converting from grams (g) to kilograms (kg), so the arrow is pointing from right to left. Enter the numbers 1, 2 and 3 according to the direction of the arrow:
2 000 1 000
, ,
kg g
0 0
kg g
2 0 0 0
kg g
kg g
Conversion from one unit to another 67
Place the decimal point after the figure 3; in this case it goes between the 2 and the first 0:
Add the new units (kg), giving an answer of 2 kilograms WORKED EXAMPLE
Convert 150 nanograms to micrograms.
METHOD ONE:MOVING THE DECIMAL POINT
You are going from a smaller unit to a larger unit, so you have to divide by 1,000, i.e.
The decimal point moves three places to the left:
0 . 1 5 0 = 0.150
METHOD TWO:USING BOXES
Place the higher unit in the left-hand box and the smaller unit in the right-handbox:
Next, add an arrow pointing in the direction of the conversion:
Next enter the numbers into the boxes, starting from the unit you are converting from, i.e. in this example from the right-hand side: the numbers are 0, 5 and 1 to give 150 nanograms:
mcg ng
1 5 0
kg g
2 .
0 3
0 2
0 1
kg g
2 0
3 0 2
0 1
mcg ng
mcg ng
150
1 000, nanograms = 0.150 micrograms
Place a zero in any empty boxes:
Now we have to decide where to place the decimal point. We are converting from nanograms (ng) to micrograms (mcg), so the arrow is pointing from right to left. Enter the numbers 1, 2 and 3 according to the direction of the arrow:
Place the decimal point after the figure 3; in this case it goes between the 0 and the 1:
Add the new units (mcg), giving an answer of 0.150 micrograms.