Metric Units and Conversions - Unitec

METRIC UNITS
The basic units of measurement are the metre (for length), the gram (for mass) and
the litre (for capacity [fluid volume]). The common metric units are set out below.
Largest
Smallest
Each prefix denotes a particular amount of the basic unit.
Mega Kilo basic unit milli micro
M K m
1,000,000 1,000
1
1,000
1
1,000,000
Examples
Kilometre (km) metre (m) millimetre (mm)
Kilogram (kg) gram (g) milligram (mg) microgram
Megawatt (MW) Litre (L) millilitre (mL) (g or mcg)
What’s great about the units above is that there is a linking factor of 1000 between a
metric unit and the metric unit next to it.
1 Kg = 1000 g 1 g = 1000 mg 1 mg = 1000 g
1 Km = 1000m 1 m = 1000 mm 1 mm = 1000 m
1 KL = 1000 L 1 L = 1000 mL 1 mL = 1000 L
1 Kg = 1000 g
1 Kg = 1000 x 1000 = 1,000,000 mg
1 Kg = 1000 x 1000 x 1000 = 1,000,000,000 g
Tucked in between Litres (L) and millilitres (mL) are two other units you will come
across in Nursing. They are the decilitre (dL) and the centilitre (cL).
L dL cL mL
(
1 10 th of a Litre) (
1 100 th of a Litre)
There is a linking factor of 10 between each of the above and the unit next to it.
1 L = 10 dL 1 dL = 10 cL 1 cL = 10 mL
1 L = 100 cL 1 dL = 100 mL
1 L = 1000 mL
Unitec: H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Metric Units.doc

METRIC UNIT CONVERSIONS
You may need to do metric unit conversions with drug calculations or with rates. In both
cases you need to know :
What metric unit you have initially and which unit you want to convert to
Whether you are converting from a Bigger unit (B) to a Smaller unit (S)
or the other way round
How many of the smaller units make up the bigger unit
If converting from a Bigger unit to a Smaller unit, you are multiplying so move the decimal
point to the Right by how many zeroes there are in the multiplier, i.e. BSR
If converting from a Smaller unit to a Bigger unit, you are dividing so move the decimal
point to the Left by how many zeroes there are in the divisor, i.e. SBL
EXAMPLES
1. How many micrograms (mcg) in 2.8 mg?
Remember mcg is the same as g
converting from mg to mcg
bigger to smaller so BSR
1 mg = 1000 mcg so move decimal point three places to the right
(since 1000 has three zeroes)
2.8 mg = 2800. g which is 2800 g
2. 965 dL is equivalent to how many mL?
converting from dL to mL
bigger to smaller so BSR
1 dL = 100 mL so move the decimal point two places to the right
965 dL = 965. dL = 96500. mL which is 96500 mL
3. How many grams in 750 g ?
converting mcg to g
smaller to bigger so SBL
1g = 1,000,000 mcg so move the decimal point six places to the left
750 mcg = 750. mcg = .000750 g
Unitec: H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Metric Units.doc

METRIC CONVERSIONS IN RATES
4. Convert 6.6 L/min to mL/min. (Here you have to convert 6.6 L to mL)
converting from L to mL
bigger to smaller so BSR
1 L = 1000 mL so move decimal point three places to the right
6.6 L = 6600. mL = 6600 mL
So 6.6 L/min = 6600 mL/min.
5. Change 350 mcg/dL into mg/dL. (You have to convert 350 mcg to mg)
converting from mcg to mg
smaller to bigger so SBL
1 mg = 1000 mcg so move the decimal point three places to the left
350 mcg = 350. mcg = .350 mg (which can be written as 0.35 mg)
So 350 mcg/dL = 0.35 mg/dL
METRIC CONVERSIONS IN DRUG CALCULATIONS
It is easier to convert bigger units to smaller units.
6. 0.5 mg of Neocytamen is prescribed. 250 mcg/mL is available…
convert 0.5 mg to mcg
bigger to smaller so BSR
1 mg = 1000 mcg so move the decimal point three places to the right
0.5 mg = 0 500. mcg = 500 mcg. You can now think of the problem as:
“ 500 mcg of Neocytamen is prescribed. 250 mcg/mL is available…”
7. Lasix 1 g is prescribed. 20 mg/mL is available…
convert 1 g to mg
bigger to smaller so BSR
1 g = 1000 mg so move the decimal point three places to the right
1. g = 1 000. mg. The problem now becomes:
“ Laxin 1000 mg is prescribed. 20 mg/mL is available…”
Unitec: H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Metric Units.doc

8. How much solute is required to make 1 L of 5% glucose? Remember 5% means
5 g/100mL so we need to convert 1L to mL. After the procedure as before we find
that 1 L = 1000 mL and the problem can now be re-phrased more simply as:
“How much (what mass/weight of) solute is required to make 1000 mL of solution if
5 g of solute is required for 100 mL?”
EXERCISE 1
Change to Change to Change to Change to Change to
milligrams grams milligrams millilitres Litres
1 4 g 6000 mg 825 mcg 2 L 4000 mL
2 8.7 g 865 mg 750 mcg 30 L 10000 mL
3 0.69 g 70 mg 65 mcg 1.5 L 625 mL
4 0.02 g 5 mg 95 mcg 4.5 L 359 mL
5 0.035 g 7259 mg 10 mcg 1.6 L 95 mL
6 0.006 g 95 mg 5 mcg 2.24 L 60 mL
7 0.655 g 2 mg 200 mcg 0.8 L 5 mL
8 4.28 g 125 mg 30 mcg 0.75 L 2 mL
EXERCISE 2
Change to
grams
Change to
millilitres
Change to
centilitres
Change to
decilitres
1 3 Kg 3 L 85 mL 8.3 L 2 g
2 6.5 Kg 25 cL 6 dL 0.9 L 2 Kg
Change to
milligrams
3 500 mg 600 dL 0.5 L 63 cL 0.43 g
4 2000 mg 3.1 dL 0.2 mL 0.75 cL 0.825 Kg
5 45 mg 0.45 cL 0.09 dL 806 mL 125 mcg
6 100 mcg 0.25 L 1.8 L 0.1 mL 8 mcg
7 24000 mcg 0.075 cL 512 mL 437 cL 0.035 g
8 6000000 mcg 546 cL 0.04 L 6000 mL 10.4 mcg
ANSWERS
EXERCISE 1 EXERCISE 2
mg g mg mL L g mL cL dL mg
1) 4000 6 0.825 2000 4 1) 3000 3000 8.5 83 2000
2) 8700 0.865 0.75 30000 10 2) 6500 250 60 9 2000000
3) 690 0.07 0.065 1500 0.625 3) 0.5 60000 50 6.3 430
4) 20 0.005 0.095 4500 0.359 4) 2 310 0.02 0.075 825000
5) 35 7.259 0.01 1600 0.095 5) 0.045 4.5 0.9 8.06 0.125
6) 6 0.095 0.005 2240 0.06 6) 0.0001 250 180 0.001 0.008
7) 655 0.002 0.2 800 0.005 7) 0.024 0.75 51.2 43.7 35
8) 4280 0.125 0.03 750 0.002 8) 6 5460 4 60 0.0104
Unitec: H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Metric Units.doc