Systems of Measurement PDF

Systems of Measurement Because medications can be prescribed in either metric or household measurements, it is important to know equivalents between the two to calculate the dose of the prescribed medication. **50-1a The Metric System** --------------------------- The [**metric system**a system o...

Systems of Measurement Because medications can be prescribed in either metric or household measurements, it is important to know equivalents between the two to calculate the dose of the prescribed medication. **50-1a The Metric System** --------------------------- The [**metric system**a system of measurements that uses the base function of 10.](javascript://)is the primary system of measurement in medicine, based on multiples of 10. There are three basic units: - gram (g), which measures mass (weight) - liter (L), which measures volume (liquid) - meter (m), which measures length (size) The metric system adds prefixes to the basic units to indicate the value (multiple or submultiple) of the unit. For example, when the prefix *kilo-* is added to the unit *meter*, it becomes *kilometer*, which has a value of 1,000 meters. [Table 50--1](javascript://) lists common prefixes in the metric system, with their values. ### **Metric System Prefixes** -- -- -- -- -- -- **50-1b Household Measures** ---------------------------- Patients at home typically use household measurements such as tablespoon and teaspoon ([Figure 50--1](javascript://)). It is important to understand these measurements so you can explain to patients how to take their medications after discharge. The basic units of this system are: - drop (gtt) - teaspoon (t or tsp) tablespoon (T or tbs) - ounce (fluid) (fl oz) - cup - pint (pt) - quart (qt) - ounce (weight) (oz) - pound (lb) **Figure 50--1** Standard measuring spoons. [Table 50--2](javascript://) shows common metric system-to-household equivalents of these units. ### **Metric System to Household Equivalents** -- -- -- -- -- -- -- -- -- -- 50-1c The Apothecary System The apothecary system was the first system of medication measurement and was developed hundreds of years ago. It consists of several measurements of volume that in the past have been used for prescribing and measuring drugs. Although this system is not commonly used in today's medical office, you should be familiar with the basic units of it, which follow: grain (gr) quart (qt) pint (pt) ounce or fluid ounce (oz) dram Minim 50-2 Review of Basic Math Basic math functions are used in everyday practice. Review Figure 50--2, which illustrates the placement of whole numbers and decimalsnumbers that are expressed as a fraction of a part using 10 as its base number; it also refers to the period used to separate a whole number from a fraction, as in 10.2, otherwise read as "ten and two-tenths.". Knowing the place values of numbers is the key to reading and writing numbers and decimals accurately. Figure 50--2 Whole numbers and decimals. An illustration shows how to read whole numbers and decimals. An upward arrow at the center corresponding to a decimal point represents the center of decimal system. A leftward arrow labeled increasing value corresponds to whole numbers on the left side of the decimal point. A rightward arrow labeled decreasing value corresponds to fractions on the right side of the decimal point. 7 zeros correspond to whole numbers and they are labeled in the following order starting from the right to the left: Ones (or units), Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, and Millions. There are two comas one after the first zero from the left and the other after the fourth zero from the left. 3 zeros correspond to fractions and they are labeled in the following order starting from the left to the right: Tenths, Hundredths, Thousandths. Then look at Tables 50--3 and 50--4, which provide solved examples of everyday mathematic functions. Consider substituting any set of numbers and solving for the answer and then check the solution with a calculator. Practice by solving the sample problems found in the accompanying workbook. Table 50--3 Review Examples of Math Problems STEPS IN ADDITION Step 1. Add the numbers in the ones column. (Add the first two numbers , then add the third number. This means that we will keep the 2 as the final number in the ones column and carry over the 1 to the tens column. Step 2. Add the numbers in the tens column. (Do not forget to carry the 1\* over from the ones column.). Step 3. There are no numbers to add in the hundreds column, so bring down the number in the hundreds place, 1. Final answer: 172 STEPS IN SUBTRACTION Step 1. Subtract the numbers in the ones column (6--8). Because 8 is greater than 6, we must convert 6 to 16 by borrowing 10 from the tens place. Now we can subtract,. Step 2. Subtract the numbers in the tens column, remembering that 4 has been reduced to 3 (because we borrowed for the ones place). So,. Step 3. Subtract the numbers in the hundreds column.. Final answer: 228 STEPS IN MULTIPLICATION Step 1. Multiply 5 by the number in the ones column:. Enter the 0 in the ones column and carry over the 2 to be added to the product of the tens column. Step 2. Multiply 5 by the number in the tens:. Now, add the number carried over from the ones column (2):. Step 3. Finally, multiply 5 by the number in the hundreds column:. Enter that number in the hundreds and thousands columns. Final answer: 2570 STEPS IN DIVISION Step 1. Read the problem (i.e., 528 divided by 32) and identify the divisorthe number used to divide into another number.and dividendthe result of dividing one number by another.. The divisor is the number after "divided by" and goes outside of the bracket (32). The dividend is the number before "divided by" and goes inside the bracket (528). Step 2. Divide 32 into the first two numbers of the dividend, 52. 32 goes into 52 evenly one time, so put 1 on the top of the bracket, and put 32 (1 × 32) beneath the 52. Step 3. Subtract 32 from. Step 4. Bring down the next digit, 8, making 208. Step 5. Divide 32 into 208. 32 goes into 208 six times evenly, so put 6 on the top of the bracket and put 192 (6 × 32) beneath the 208. Step 6. Subtract 192 from. Step 7. Add a decimal point and a zero. This does not change the value of the dividend but allows you to continue dividing. Step 8. Bring the 0 down, making 160. Step 9. Divide 32 into 160. 32 goes into 160 five times evenly, so put 5 on top of the bracket, and put 160 (5 × 32) beneath the 160. Step 10. Subtract 160 from. Final answer: 16.5 Table 50--4 General Rules for Working with Decimals ADDING DECIMALS Step 1. Line up the decimal points for each number. Step 2. Add columns starting on the right. Work from the top down. Final answer: 198.33 SUBTRACTING DECIMALS Step 1. Line up the decimal points for each number. Step 2. Subtract columns starting on the right. Borrow from the number place to the left when needed. Final answer: 688.755 MULTIPLYING DECIMALS Step 1. Temporarily disregard the decimal points and multiply as you would a whole number. Step 2. Count the number of decimal places in the numbers being multiplied. In this example, the total number of decimal places is three. Step 3. In your product, move the decimal point over number of total decimal places. Final answer: 143.045 DIVIDING DECIMALS Step 1. Read the problem (i.e., 52.8 divided by 0.32) and identify the divisor and dividend. The divisor is the number after "divided by" and goes outside of the bracket (0.32). The dividend is the number before "divided by" and goes inside the bracket (52.8). Step 2. Now, move the decimal point to the right in the divisor until it becomes a whole number. In this example, you would move the decimal two places. Step 3. Now, move the decimal point in the dividend the same number you moved the divisor. Step 4. Divide as you normally would. Final answer: 165 Fractions A fraction, like a decimal, indicates part of a whole number, for example: 1/2, 5/6, or 12/100. The top number of a fraction is called the numerator; the bottom number is called the denominator. An improper fraction indicates that the numerator is larger than the denominator, for example: 12/8 or 141/13. A mixed fraction includes both a whole number and a fraction, for example: 3-1/2, 24-3/8. When solving a problem with a mixed fraction, begin by converting the whole number into an improper fraction, using the formula: (\[whole number × denominator\] + numerator)/denominator. Example Convert 5-2/3 to an improper fraction. Step 1. Identify the numbers to plug into the equation. The whole number is 5; the denominator is 3; the numerator is 2. Step 2. Plug the numbers into the preceding formula and calculate:. Step 3. Add the denominator, which is 3. Final answer: 17/3. Table 50--5 reviews adding, subtracting, multiplying, and dividing fractions. 50-2b Percentages Percent means "per hundred," and a percentage expresses a value that is part of 100. For instance, 75% means 75/100 or 0.75. When the word of is used in conjunction with percent, it means to multiply. Before calculating percentages, change the percent number to a decimal (by dividing by 100). Then multiply the numbers together. Example 50-2c Ratios A ratio expresses a relationship between two components and is an alternate way to express a fraction. It contains two numbers separated by a colon. The numerator is to the left of the colon, and the denominator is to the right. Example A ratio is written as 1:20. The same ratio is spoken as "One to twenty." The same ratio, expressed as a fraction, would be 1/20. The same ratio, expressed as a decimal, would be 0.05. The same ratio expressed as a percent would be 5%. **50-2d Proportions** --------------------- A [**proportion**another way of saying fraction.](javascript://)expresses the relationship between two ratios. Two ratios are set, side by side, with either an equal sign (=) or a colon (:) between them. The values within a proportion are called [**means**the average that is derived by adding up all the values of a given series and dividing by the number of values.](javascript://)and [**extremes**the highest or lowest level of a math function on an interval.](javascript://). The means are the numbers directly to the left and right of the equal sign. The extremes are the two outer numbers. In a true proportion, the product of the means equals the [**product**the result of multiplying two numbers together.](javascript://)of the extremes. In the example we have been using, 2 × 6 is equal to 1 × 12. Understanding proportion is important because it allows you to solve for an unknown amount, (x), when the other values are known. This concept is critical to determining dosage calculations. Main content 50-3 Dosage Calculations Basic math skills are necessary for accurately calculating and verifying medication dosages to ensure patient safety before administering any medication. The wrong dose of any medication can have profound adverse consequences. Insufficient dosing of an antibiotic does nothing to cure an infection, but an excess dose can cause a toxic reaction. Calculating the right dose of medication is a responsibility not to be taken lightly. Familiarity with fractions and equation solving is necessary to convert and calculate drug dosages. Several methods can be used to calculate dosages; this book will present two, the basic formula method and the ratio and proportion method. The examples for each method will use the same orders and supply numbers, so you can easily compare the methods. **50-3a Basic Formula** ----------------------- The bsic formula method is: The letters inthe formula stand for: The amount *Needed* is the dose prescribed, or what the provider has ordered. The amount *Available* is the supply on hand (from the medication label). The *Vehicle* is the form and amount in which the medication comes (capsule, tablet, liquid).