Chapter 25 Basic math calculations

This chapter covers basic math calculations that dialysis personnel may need to use while providing care to patients in a chronic or acute dialysis setting. Working with numbers and calculations can sometimes induce anxiety in even the most seasoned student or practitioner. Being able to convert numbers and perform math calculations is critical to safely administering the correct dosage of medication or determining a patient’s dialysis treatment prescription. It is imperative that you are able to correctly calculate medication dosages to ensure that your patient is appropriately treated. You will have the opportunity to review basic math skills and practice some problems to strengthen your skills and increase your comfort level in working with numbers and calculations.

The metric system

The metric system is the most widely used system of measurement in the world. In healthcare, it is the most commonly used system to measure medications. It is well suited for this purpose because it can be used to name very large numbers and, more importantly, very small numbers. The three base units used in the metric system are the meter, liter, and gram. The gram (g) is used to measure weight, the liter (L) is used to measure volume, and the meter (m) is used to measure length. You will most often use grams and liters to calculate medication dosages and meters to measure for height or size (Boxes 25-1 and 25-2).

Box 25-1 Common Conversions Used in Healthcare

1 oz = 30 mL

1 L = 1000 mL

1 g = 1000 mg

1 mg = 1000 mcg

1 kg = 2.2 lb or 1000 mL

Box 25-2 Common Abbreviations Used in Healthcare

kg = kilogram

g = gram

mg = milligram

mcg = microgram

mL* = milliliter

cc* = cubic centimeter

^* mL and cc are used interchangeably

You will use the metric system not only to calculate medication dosages, but also to calculate your patient’s treatment parameters. For example, a patient’s weight is always converted into kilograms when determining how much fluid the patient gained interdialytically, how much over “dry” weight the patient is, and how much fluid was removed intradialytically.

How do you convert units within the metric system?

It is easy to convert units within the metric system when you reference the metric line, which is illustrated on the next page. Make note of the base units in the center of the metric line: meter, gram, and liter. Everything to the left of the base unit gets larger and is represented by a whole number. Everything to the right of the base unit gets smaller and is represented by fractions of whole numbers. Prefixes are used with the base units to determine whether the units are larger or smaller than the base unit. The prefixes indicate the size of the unit in multiples of ten. The size of a base unit can be changed by multiplying or dividing by 10. When converting larger units to smaller units, multiply by ten, or move the decimal point to the right for each unit changed; when converting smaller units to larger units, divide by ten, or move the decimal point to the left for each unit changed. The prefixes in the metric line are based on powers of 10. When you make a conversion within the metric system, you multiply or divide by powers of 10. A move from one prefix to another is either 10 times larger or 10 times smaller.

1 meter is equal to 10 decimeters, 100 centimeters, and 1000 millimeters. For example, centimeters are 10 times larger than millimeters; therefore, 1 centimeter equals 10 millimeters. Because centimeters are larger than millimeters, it takes more millimeters to make up the same length.

For each “step” to the right along the metric line, you multiply by 10. For example, if you want to go from a base unit of liters (L) to centiliters (cL), use the following conversion:

If you want to go from a base unit of grams (g) to milligrams (mg), use the following conversion:

Convert 4 liters (L) to milliliters (mL)

Multiply 4 L by 1000

4 L × 1000 = 4000 mL

or

Move the decimal point three places to the right* to give you 4000 mL

^* You may need to fill in zeros to reach the new decimal point.

Convert 4000 milliliters (mL) to liters (L)

Divide 4000 mL by 1000

4000 mL ÷ 1000 = 4 L

or

Move the decimal point three places to the left to give you 4 L

In answers that contain only a decimal (e.g., .5 mg), place a zero to the left of the decimal point. This will prevent any errors from occurring should the decimal point go unrecognized. The difference between administering a 5 mg dose and a 0.5 mg dose is significant.

When you make a conversion within the metric system, you move the decimal point one place for each “step” that you move on the metric line. If you move to the right on the metric line, you move the decimal point to the right. If you move to the left on the metric line, you move the decimal point to the left.

An example of how to convert meters (m) to decimeters (dm), centimeters (cm), and millimeters (mm) follows:

Convert 5 m to dm

or

Convert 5 m to cm

or

Convert 5 m to mm

or

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