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# Clinical Calculations: Module 3: The Metric System

## The Metric System

### Module 3 - The Metric System of Measurement and Conversions Using the Metric system

What’s in this module?

Most of the world uses the metric system of measurement.  The United States is one of the very few exceptions.  We tend to use the household system of measurement in everyday situations. In the United States, the metric system tends to be used primarily in scientific and medical settings.

As a nurse, you will use the metric system in almost everything you do.  Medication orders are stated using the metric system with very few exceptions.  If you learn the relationships between the units of the metric system, converting units of measurement will be easy for you.

Summary of problem types in this module

In this module you will be working problems to change from one unit of measurement in the metric system to another unit of measurement.

Let’s look at the basics of the metric system: The metric system has three measurement bases, or basic units: meters (length), liters (volume), and grams (weight or mass). The prefixes in front of the base measurement tell you whether the amount is larger or smaller than the base measurement and how much larger or smaller.  Kilo- represents the largest unit on the chart, while milli- represents the smallest unit on the chart.  Conversions within a base of measure can be made by moving the decimal place.

Need an easy way to remember the relative sizes of the metric units?  Remember King Henry Died by Drinking Chocolate Milk. Equivalents to know

Conversion between the metric system and the system commonly used in the United States will be introduced as needed in later modules.  Illustrations of metric measurements are shown for reference.

These equivalents are the most commonly used in nursing:

WEIGHT MEASUREMENTS (Gram is the measurement base)

1 kg (kilogram) = 1000g (Note: g, G, Gm, gm are all abbreviations for gram)

1 g (gram) = 1000 mg (milligrams)

1 mg (milligram) = 1000 mcg (micrograms) VOLUME MEASUREMENTS (Liter is the measurement base)

1 L (liter) = 1000 ml (milliliters) LENGTH MEASUREMENTS (Meter is the measurement base.)

1 meter = 100 cm (centimeters)

1 cm (centimeter) = 10 mm (millimeters) EQUIVALENTS ACROSS SYSTEMS

1 kg (kilogram) = 2.2 lb (pounds)

5 ml (milliliter) = 1 tsp (teaspoon)

30 ml (milliliter) = 1 oz (ounce)

2.5 cm (centimeters) = 1 inch

Converting temperature

Hospitals and emergency services often use the Celsius system of measuring temperature instead of the Fahrenheit system more familiar to us in the United States.  The most frequent example of the use of Celsius in the medical setting is the measurement of body temperature.  Storage temperatures for medication and other substances may also be stated in Celsius.

This type of conversion is a situation in which you will need to remember a formula. Converting to military time

Military time is used by many hospitals and emergency services.  Military time reduces ambiguity because the A.M. and P.M. designations are not needed.  Colons are also not needed in recording military time.  Times are always recorded as four digits.

Times before 1:00 P.M. need no conversion.  Simply omit the colon and the A.M. designation. Afternoon and evening times starting with 1:00 P.M. are found by adding 1200 to the conventional time used in the United States.  Example:  1200 + 0100 = 1300; 1:00 P.M. is written as 1300.

The colon and the P.M. designation are omitted.  Times at or after 1300 are understood to be afternoon.  Midnight may be written as 0000 or 2400.  Follow the convention of the institution where you work when recording midnight.

Here are some easy examples:

12:00 noon  =  1200  (nothing is added to noon)

12:01 A.M. =  1201  (nothing is added to minutes after noon)

2:30 P.M. + 1200 = 1430 (the military time equivalent)

11:59 P.M. + 1200 = 2359 (the military time equivalent) Rounding rules to know

Only these general rounding rules for decimals will apply to this module.

1. If the answer is less than one (1), take the math out three (3) places past the decimal point (the thousandth position) and round to two (2) places past the decimal point (the hundredth position).

2. If the answer is greater than one (1), take the math out two (2) places past the decimal point (the hundredth position) and round to one (1) place past the decimal point (the tenth position).

3. Do not include trailing zeros. (Ex: 12.0 ml would simply be expressed as 12 ml and 0.40 mg would be expressed as 0.4 mg)

4. Always use a leading zero for numbers less than one. (Ex: .25 ml should be expressed as 0.25ml)

The starting factor (SF) is the amount you start with  - the quantity and the units you know.  It is the quantity and unit of measurement to be converted.

The answer unit (AU) is the equivalent quantity expressed in the units that you have available.  The AU is the unit of measurement you have in an amount equivalent to the SF (the amount you know).

Problem Type 1 –Conversions within the Metric System

A medication strength is listed as 0.25 mg per ml.  How many mcg are in one ml?

Here’s the problem set up in the dimensional analysis format:

SF = 0.25 mg

AU = mcg

Equivalent:

1 mg = 1000 mcg

Equation: Note that conversions within a base unit of the metric system can be done by simply moving the decimal point:

0.25 mg = 250 mcg (The decimal is moved three places to the right) Here’s another example:

A medication is ordered at 500 mg per dose.   The dosage strength is 150 mg per ml.  How many ml will be given per dose?

This problem requires a conversion between weight and volume bases in the metric system.

SF = 500 mg

AU = ml

Equivalent:

1 ml = 150 mg

Equation: Note that the rounding rule for numbers >1 is used.  If you check your answer,

3.3 ml X 150 mg per ml  = 495 mg per dose

This answer is a close approximation to the actual dose ordered.  Measuring instruments for liquid medication can usually not be measured more closely than a tenth of a ml.

Problem Type 2 – Conversions Between the Metric System and the Household System

A nurse has measured the length of a wound as 4 inches.  How many cm long is the wound?

Here’s the problem set up in the dimensional analysis format:

SF = 4 in

AU = cm

Equivalent:

2.5 cm (centimeters) = 1 inch

Equation: Here’s another example:

A child weighs 56 lb.  A medication is ordered by weight in kg.  How many kg does the child weigh?

SF = 56 lb

AU = kg

Equivalent:

1 kg (kilogram) = 2.2 lb (pounds)

Equation: Use the rounding rule for numbers >1.

Problem Type 3 –Conversion of temperature

Examples:

A nurse has measured a client’s temperature as 99.5 degrees F using a thermometer with only the Fahrenheit scale.  How many degrees Celsius is the temperature?

Formula:

(Degrees F – 32) X 0.5556 = Degrees C

Equation: Use the rounding rule for numbers >1.

Here’s another example:

A solution needs to be stored at 20 degrees C.  At what temperature should the storage unit be using the Fahrenheit scale?

Formula:

(Degrees C X 1.8) + 32 = Degrees F

Equation: Use the rounding rule for numbers >1.

Problem Type 4 –Conversion of time

An intravenous solution started running at 8:00 A.M.  The solution will take 10 hours to complete.  At what time will the solution be finished (in military time)?  Convert the time back to standard time as used in the United States in order to inform the client’s family when the solution will be finished.  Here’s another example:

A medication is to be given every 6 hours.  The first dose was given at 6:00 P.M.  When should the next four doses be scheduled?    For as long as the client takes this medication, the doses will be scheduled to be given at 1800, 2400 (0000), 0600, and 1200.  These times will be recorded on the client’s medication schedule in a hospital setting.

The outpatient client will be told to take the medication at 6:00 P.M., 12:00 A.M., 6:00 A.M., and 12:00 P.M.

## Practice Problems

### Module 3 Practice Problems

Basic Conversions within the Metric System

1. Convert 500 mg to g

2. Convert 0.35 mg to mcg

3. Convert 0.5 kg to g

4. Convert 1500 mcg to mg

5. Convert 350 ml to L

6. Convert 0.33 L to ml

7. Convert 55 mm to cm

8. Convert 0.5 cm to mm

Conversions Between the Household System and the Metric System

9. Convert 159 lb to kg

10. Convert 110 kg to lb

11. Convert 32 oz to kg

12. Convert 10 oz to lb

13. Convert 0.25 lb to oz

14. Convert 250 oz to lb

15. Convert 2 tsp to ml

16. Convert 6 ml to tsp

17. Convert 75 ml to oz

18. Convert 105 ml to oz

19. Convert 30 oz to cups

20. Convert 0.25 qt to oz

21. Convert 600 oz to L

22. Convert 35 oz to ml

23. Convert 45 mm to in

24. Convert 0.25 cm to mm

25. Convert 0.5 in to cm

Conversions in the Medical Environment

26. A nurse needs to give 500 mg of a medication.  The dosage strength is 150 mg per ml.  How many ml of the medication should the nurse give?

27. A client has been ordered 1 g of a medication that comes in 250 mg tablets.  How many tablets should the nurse give to the client?

28. A client is on a fluid-restricted diet and can have only 1 L of fluids per day, including liquid meals.  How many cans of a nutritional formula can the client have if each can of formula contains 1 cup?

29. A juvenile client is to be given 250 mg per kg of weight of a medication.  The strength of the medication is 500 mg per oz.  The client weighs 62 lb.  How many oz of the medication should the nurse give to the client?  (Use the client’s weight in lb as your SF.)

30. An IV infusion is to start at 0130 and run at 100 ml per hour. There are 1000 ml of fluid.  At what time will the infusion end?

31. A medication is to be given 6 times per day (1 day = 24 hrs).  The medication can start at 0500.  What is the daily medication schedule for this medication?

32. A client is admitted to the hospital at 1235.  The assessment nurse must finish the client’s admission within 2.5 hours.  What is the nurse’s deadline for completing the admission?

33. A client has a temperature of 101.5 degrees F.  The healthcare provider wants to be called if the client’s temperature rises above 38 degrees C.  Should the healthcare provider be called?

34. A client is to be chilled during cardiac surgery to 36 degrees C.  What is the client’s  temperature on the Fahrenheit scale?

35. A medication needs to be stored at 65 degrees F.  The medication room refrigerator only has a Celsius thermometer.  What is 65 degrees F on the Celsius scale?

### Answers to Module 3 Practice Problems

Basic Conversions within the Metric System

1. Convert 500 mg to g.

Here is the problem worked out with dimensional analysis:

SF = 500 mg

AU = g

Equivalent:

1 g = 1000 mg

Equation: Note that conversions within a base unit of the metric system can be done by simply moving the decimal point.  See the Metric Conversion Chart in the content area of this module.

500 mg = 0.5 g

(The decimal is moved three places to the left because the unit g is 1000 times larger than the unit mg).

2. Convert 0.35 mg to mcg.

SF = 0.35 mg

AU = mcg

Equivalent:

1 mg = 1000 mcg

Equation: OR simply move the decimal point three places to the right because the unit mcg is 1000 times smaller than the unit mg.

0.35 mg = 350 mcg

3. Convert 0.5 kg to g.

SF = 0.5 kg

AU = g

Equivalent:

1 kg = 1000 g

Equation: Or simply move the decimal point if you can do so with confidence. The decimal point is moved three places to the right because the unit gram is 1000 time smaller than the unit kilogram.

0.5 kg = 500 g

4. Convert 1500 mcg to mg.

SF = 1500 mcg

AU = mg

Equivalent:

1 mg = 1000 mcg

Equation: Or simply move the decimal point if you can do so with confidence:

1500 mcg = 1.5 mg

5. Convert 350 ml to L.

SF = 350 ml

AU = L

Equivalent:

1 L = 1000 ml

Equation: Or simply move the decimal point if you can do so with confidence:

350 ml = 0.35 L

6. Convert 0.33 L to ml.

SF = 0.33 L

AU = ml

Equivalent:

1 L = 1000 ml

Equation: Or simply move the decimal point if you can do so with confidence:

0.33 L = 330 ml

7. Convert 55 mm to cm.

SF = 55 mm

AU = cm

Equivalent:

1 cm = 10 mm

Equation: Or simply move the decimal point if you can do so with confidence:

55 mm = 5.5 cm

8. Convert 0.5 cm to mm.

SF = 0.5 cm

AU = mm

Equivalent:

1 cm = 10 mm

Equation: Or simply move the decimal point if you can do so with confidence:

0.5 cm = 5 mm

Confused?  Go back to the content section above and review the charts about the metric system again.

You’ll be seeing the metric system in almost all the problems in the remaining units.

Conversions Between the Household System and the Metric System

9. Convert 159 lb to kg.

SF = 159 lb

AU = kg

Equivalent:

1 kg = 2.2 lb

Equation: Remember your rounding rule for numbers >1.

10. Convert 110 kg to lb.

SF = 110 kg

AU = lb

Equivalent:

1 kg = 2.2

Equation: 11. Convert 32 oz to kg.

SF = 32 oz

AU = kg

Equivalents:

16 oz = 1 lb

2.2 lb = 1 kg

Equation: As long as you remember to set up the equation so that the unwanted units of measurement cancel each other, you will find the answer no matter how many equivalents you have.

Remember your rounding rule for numbers <1.

12. Convert 10 oz to lb.

SF = 10 oz

AU = lb

Equivalent:

1 lb = 16 oz

Equation: 13. Convert 0.25 lb to oz.

SF = 0.25 lb

AU = oz

Equivalent:

1 lb = 16 oz

Equation: 14. Convert 250 oz to lb.

SF = 250 oz

AU = lb

Equivalent:

1 lb = 16 oz

Equation: Remember your rounding rule for numbers >1.

15. Convert 2 tsp to ml.

SF = 2 tsp

AU = ml

Equivalent:

1 tsp = 5 ml

Equation: 16. Convert 6 ml to tsp.

SF = 6 ml

AU = tsp

Equivalent:

1 tsp = 5 ml

Equation: 17. Convert 75 ml to oz.

SF = 75 ml

AU = oz

Equivalent:

1 oz = 30 ml

Equation: 18. Convert 105 ml to oz.

SF = 105 ml

AU = oz

Equivalent:

1 oz = 30 ml

Equation: 19. Convert 30 oz to cups.

SF = 30 oz

AU = cups

Equivalent:

8 oz = 1 cup

Equation: 20. Convert 0.25 qt to oz.

SF = 0.25 qt

AU = oz

Equivalent:

1 qt = 32 oz

Equation: 21. Convert 600 oz to L.

SF = 600 oz

AU = L

Equivalents:

1 oz = 30 ml

1000 ml = 1 L

Equation: 22. Convert 35 oz to ml.

SF = 35 oz

AU = ml

Equivalent:

1 oz = 30 ml

Equation: 23. Convert 45 mm to in.

SF = 45 mm

AU = in

Equivalents:

1 in = 2.5 cm

1 cm = 10 mm

Equation: 24. Convert 0.25 cm to mm.

SF = 0.25 cm

AU = mm

Equivalent:

1 cm = 10 mm

Equation: 25. Convert 0.5 in to cm.

SF = 0. 5 in

AU = cm

Equivalent:

1 in = 2.5 cm

Equation: Conversions in the Medical Environment

26. A nurse needs to give 500 mg of a medication.  The dosage strength is 150 mg per ml.  How many ml of the medication should the nurse give?

SF = 500 mg

AU = ml

Equivalent:

1 ml = 150 mg

Equation: 27. A client has been ordered 1 g of a medication that comes in 250 mg tablets.  How many tablets should the nurse give to the client?

SF = 1 g

AU = tablets

Equivalents:

1 tablet = 250 mg

1 g = 1000 mg

Equation: 28. A client is on a fluid-restricted diet and can have only 1 L of fluids per day, including liquid meals.  How many cans of a nutritional formula can the client have if each can of formula contains 1 cup?

SF = 1 L

AU = cans

Equivalents:

1 can = 1 cup

1 cup = 8 oz

1 oz= 30 ml

1000 ml = 1 L

Equation: 29. A juvenile client is to be given 250 mg per kg of weight of a medication.  The strength of the medication is 500 mg per oz.  The client weighs 62 lb.  How many oz of the medication should the nurse give to the client?  (Use the client’s weight in lb as your SF.)

SF = 62 lb

AU = oz

Equivalents:

2.2 lb =1 kg

1 kg=250 mg

500 mg = 1 oz

Equation: 30. An IV infusion is to start at 0130 and run at 100 ml per hour. There are 1000 ml of fluid.  At what time will the infusion end?

There are two steps to this problem. First you must determine how long it will take for the fluids to infuse. Then you must determine what time the infusion will end.

SF = 1000 ml

AU = hr

Equivalent:

100 ml = 1 hr

Equation: The fluid will start at 0130 and run for 10 hours. 31.  A medication is to be given 6 times per day (1 day = 24 hrs).  The medication can start at 0500.  What is the daily medication schedule for this medication?

Six times per day means the medication will be given every four hours. To calculate the medication schedule, use 0400 for the interval between doses.     Doses will be scheduled for 0500, 0900, 1300, 1700, 2100, and 0100.

32. A client is admitted to the hospital at 1235.  The assessment nurse must finish the client’s admission within 2.5 hours.  What is the nurse’s deadline for completing the admission? (the answer of 1465 is the same as 1505 – the extra 60 minutes advances the hour to the next hour)

33. A client has a temperature of 101.5 degrees F.  The healthcare provider wants to be called if the client’s temperature rises above 38 degrees C.  Should the healthcare provider be called?

Conversion of temperature from Fahrenheit to Celsius.  Yes, the healthcare provider should be called.

34. A client is to be chilled during cardiac surgery to 30 degrees Celsius.  What is the client’s temperature on the Fahrenheit scale?

Conversion of temperature from C to F.   35.  A medication needs to be stored at 65 degrees Fahrenheit.  The medication room refrigerator only has a Celsius thermometer.  What is 65 degrees Fahrenheit on the Celsius scale?

Conversion of temperature from F to C.  