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Conversions: Between and Within Systems
Revised KBurger0808
Textbook Assignment:
Pickar, G. (2007). Dosage calculations: A ratio-proportion approach. (2nd ed.)Chapter 4
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Equivalents1 grain (gr) = 60 milligrams (mg)1 teaspoon (t) = 5 milliliters (mL)
1 tablespoon (T) = 3 teaspoons (t)1 ounce (oz) = 30 milliliters (mL)
1 cup = 8 ounces (oz)1 Kilogram (Kg) = 2.2 pounds (lbs)
1 liter (L) = 1000 milliliters (mL)1 gram (g) = 1000 milligrams (mg)
1 milligram (mg) = 1000 micrograms (mcg)
The equivalents listed in blue are only considered approximate equivalents
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Converting Using Ratio-Proportion
• Rule– Recall equivalents– Set up a proportion of two equivalent ratios– Cross-multiply to solve for an unknown quantity, X
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Converting Using Ratio-Proportion
• Remember– Each ratio in a proportion must have the same
relationship and follow the same sequence– A proportion compares like things to like things
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Converting Using Ratio-Proportion
• Remember– The units of measurement in both numerators and
denominators must match– ALWAYS, ALWAYS, ALWAYS label the
measurement units in each ratio INCLUDING your unknown quantity X
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Converting Using Ratio-Proportion
• Example– How many feet are in 36 inches?
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1 foot = 12 inches
1 ft
12 inX ft
36 in
12X 36
12X
12
36
12
X 3 feet
Converting Using Ratio-Proportion• Recall equivalent
• Set up a proportion of two equivalent ratios
• Cross multiply to solve for “X”
• Label units to match the unknown “X”
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1 gm=1,000 mg
1 gm
1,000 mg
5g
X mg
X 1,000 5
X 5,000 mg
Using Ratio Proportion to Convert Within Metric System
• Recall equivalent
• Set up a proportion of two equivalent ratios
• Cross multiply to solve for “X”
• Label units to match unknown “X”
EXAMPLE: Convert 5 grams to milligrams
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Converting Within the Metric System
Short Cut• Medication conversions within the metric system
most often occur between: mg and mcg [ mg are larger than mcg ] g and mg [ g are larger than mg ] L and mL [ L are larger than mL]
• These are all 3 decimal place differences[ a difference of 1000 ]
• To use this Short Cut you will need to remember-which unit is larger-to always move 3 decimal places
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Conversion Slide• Keep this visual in mind when
converting within the metric system
kg g mg mcg
Move decimal point three places between each unit
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Converting Within Metric SystemShort Cut continued
• Write out the desired equivalent in this format 5 mg = ______ mcg
• Then draw an arrow that starts at the larger unit and points toward the smaller unit Larger to Smaller
• Move the decimal point in the direction of the arrow by three places.
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Calculating a Drug Dosage that requires Conversion between Systems
• Drug order reads Codeine sulfate gr ¾ p.o. q.4h p.r.n., pain
• Drug supplied is Codeine sulfate 30 mg per tablet• Calculate one dose
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Converting to Same System
• Drug order reads Codeine sulfate gr ¾ p.o. q.4h p.r.n., pain
• Drug supplied is Codeine sulfate 30 mg per tablet
• What do you notice?– Different system– Needs to be converted
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Approximate Equivalent: gr i = 60 mg
• Step 1. Convert – Convert to equivalent units in the same system
of measurement. Convert gr to mg. – Approximate equivalent: gr i = 60 mg.
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Convert usingRatio Proportion Method
• Start by writing a known ratio: 1 grain = 60 mg [ the known equivalent ]
• Then fill in the rest of the proportion• Solve for X
1 gr ¾ gr 60 mg = X mg
1X = 60 x ¾ (0.75)X = 45 mg
• Codeine gr ¾ = 45 mg
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Think
• Step 2Stop and think carefully about what a reasonable dosage should be:You have just figured out that the doctor ordered 45 mg. The drug label indicates that each tablet = 30 mg.Will you be giving more or less than 1 tablet?
MORE
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Step 3: Calculate usingRatio Proportion Method
• Start by writing known ratio from the problem• Complete the proportion with other information you have
[doctor’s order ]• Check for matching units.
Cross multiply and solve for X• 30mg 45mg 30X = 45 1 tablet = X tablet X = 45 = 1 15 = 1 ½ tablets
30 30