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A2
Math
CHANGING FRACTIONS TO DECIMALS
CHANGING FRACTIONS TO DECIMALS
To change a fraction to a decimal, divide the numerator by the denominator and add zeros as needed. If the
numerator doesn't divide evenly into the denominator, carry division three places.
Example 1:
Example 2:
Changing fractions to decimals can also be a method of comparing fraction size. The fractions being
compared are changed to decimals, and the rules relating to comparing decimals are then applied. (See
Comparing the Value of Decimals, p. 27.)
Example: Which fraction is larger, 1/3 or 1/6
Solution: 1/3 = 0.333 …as a decimal
1/6 = 0.166 …as a decimal
1/3 is therefore the larger fraction.
From: Gray Morris: Calculate with Confidence, 4th ed.
RATIOS
,RATIOS
A ratio is used to indicate a relationship between two numbers. These numbers are separated by a colon (:).
Example:
The colon indicates division; therefore a ratio is a fraction, and the numbers or terms of the ratio are the
numerator and denominator. The numerator is always to the left of the colon, and the denominator is always to
the right of the colon.
Example: 3:4 (3 is the numerator, 4 is the denominator, and the expression can be written as 3/4.)
Example: In a nursing class, if there are 25 male students and 75 female students, what is the ratio of male
students to female students? 25 male students to 75 female students = 25 male students per 75 female students
= 25/75 = 1/3. This is the same as a ratio of 25:75 or 1:3.
Ratio Measures: in Solutions
There are some medications that express the strength of the solution by using a ratio. Ratio measures are
commonly seen in solutions. Ratios represent parts of drug per parts of solution, for example 1:10,000 (this
means 1 part drug to 10,000 parts solution).
Example 1: A 1:5 solution contains 1 part drug in 5 parts solution.
Example 2: A solution that is 1 part drug in 2 parts solution would be written as 1:2.
Ratio strengths are always expressed in lowest terms.
Remember
The more solution a drug is dissolved in, the less potent the strength becomes. For example, a ratio strength of
1:1000 (1 part drug to 1000 parts solution) is more potent than a ratio strength of 1:10,000 (1 part drug in
10,000 parts solution).
From: Gray Morris: Calculate with Confidence, 4th ed.
CHANGING PERCENTAGES TO FRACTIONS, DECIMALS,
AND RATIOS
CHANGING PERCENTAGES TO FRACTIONS, DECIMALS, AND RATIOS
The percent sign may be used with a whole number (15%), a fraction (1/2%), a mixed number (14 1/2%), or a
decimal (0.6%).
To change a percent to a fraction, drop the percent sign, place the number over 100, and reduce to lowest
terms.
Example 1:
Example 2:
PRACTICE PROBLEMS
,Change the following percentages to fractions and reduce to lowest terms.
9. 1% ________________
10. 2% ________________
11. 50% ________________
12. 80% ________________
13. 3% ________________
Answers on p. 587
To change a percentage to a decimal, drop the percent sign, and move the decimal point two places to the left
(add zeros as needed).
Example 1:
Example 2:
Example 3:
Note
Example 3 is an alternative method. Drop the percent sign. Write the remaining number as the numerator.
Write “100” as the denominator. Reduce the result to lowest terms. Divide the numerator by the
denominator to obtain a decimal.
PRACTICE PROBLEMS
Change the following percentages to decimals.
14. 10% ________________
15. 35% ________________
16. 30% ________________
17. 14.2% ________________
18. ¼% ________________
Answers on p. 587
To change a percentage to a ratio, change it to a fraction and reduce to lowest terms, then place the numerator
as the first term of the ratio and the denominator as the second term. Separate the two terms with a colon (:).
Example:
, PRACTICE PROBLEMS
Change each of the following percentages to a ratio. Express in lowest terms:
19. 25% ________________
20. 11% ________________
21. 75% ________________
22. 4.5% ________________
23. ⅖% ________________
Answers on p. 587
From: Gray Morris: Calculate with Confidence, 4th ed.
HOUSEHOLD SYSTEM
HOUSEHOLD SYSTEM
The household system is an old system and the least accurate of the three systems of measure. It is a
modified system designed for everyday use at home. Nurses need to be familiar with household measures,
because clients often use utensils in the home to take prescribed medications. Capacities of utensils such as a
teaspoon, a tablespoon, and a cup vary from one house to another; therefore liquid measures are approximate.
Because of the increase in nursing care provided at home (home care, visiting nurse), it is imperative that
nurses become adept in converting from one system to another. When calculating doses or interpreting the
health care provider's instructions for the client at home, the nurse must remember that household measures
are used. Consequently the nurse must be able to calculate equivalents for adaptation in the home, even
though medication administration spoons, droppers, and medication measuring cups (Figure 7-3) are
available.
FIGURE 7-3 Medicine cup showing household/metric measurements.
Using household measures for dosage measurements can place a client at risk. Always advise clients and their
families to use the measuring devices or droppers packaged with the medication or provided by the pharmacy.
Common household measures to memorize are the following:
1 teaspoon (t, tsp) = 5 mL
1 tablespoon (T, tbs) = 15 mL
1 measuring cup = 8 oz
Note
Anything less than a teaspoon should be measured in a syringe-type device that has no needle and not a
measuring cup. Use the measuring devices packaged with the medication or provided by the pharmacy.
A2
Math
CHANGING FRACTIONS TO DECIMALS
CHANGING FRACTIONS TO DECIMALS
To change a fraction to a decimal, divide the numerator by the denominator and add zeros as needed. If the
numerator doesn't divide evenly into the denominator, carry division three places.
Example 1:
Example 2:
Changing fractions to decimals can also be a method of comparing fraction size. The fractions being
compared are changed to decimals, and the rules relating to comparing decimals are then applied. (See
Comparing the Value of Decimals, p. 27.)
Example: Which fraction is larger, 1/3 or 1/6
Solution: 1/3 = 0.333 …as a decimal
1/6 = 0.166 …as a decimal
1/3 is therefore the larger fraction.
From: Gray Morris: Calculate with Confidence, 4th ed.
RATIOS
,RATIOS
A ratio is used to indicate a relationship between two numbers. These numbers are separated by a colon (:).
Example:
The colon indicates division; therefore a ratio is a fraction, and the numbers or terms of the ratio are the
numerator and denominator. The numerator is always to the left of the colon, and the denominator is always to
the right of the colon.
Example: 3:4 (3 is the numerator, 4 is the denominator, and the expression can be written as 3/4.)
Example: In a nursing class, if there are 25 male students and 75 female students, what is the ratio of male
students to female students? 25 male students to 75 female students = 25 male students per 75 female students
= 25/75 = 1/3. This is the same as a ratio of 25:75 or 1:3.
Ratio Measures: in Solutions
There are some medications that express the strength of the solution by using a ratio. Ratio measures are
commonly seen in solutions. Ratios represent parts of drug per parts of solution, for example 1:10,000 (this
means 1 part drug to 10,000 parts solution).
Example 1: A 1:5 solution contains 1 part drug in 5 parts solution.
Example 2: A solution that is 1 part drug in 2 parts solution would be written as 1:2.
Ratio strengths are always expressed in lowest terms.
Remember
The more solution a drug is dissolved in, the less potent the strength becomes. For example, a ratio strength of
1:1000 (1 part drug to 1000 parts solution) is more potent than a ratio strength of 1:10,000 (1 part drug in
10,000 parts solution).
From: Gray Morris: Calculate with Confidence, 4th ed.
CHANGING PERCENTAGES TO FRACTIONS, DECIMALS,
AND RATIOS
CHANGING PERCENTAGES TO FRACTIONS, DECIMALS, AND RATIOS
The percent sign may be used with a whole number (15%), a fraction (1/2%), a mixed number (14 1/2%), or a
decimal (0.6%).
To change a percent to a fraction, drop the percent sign, place the number over 100, and reduce to lowest
terms.
Example 1:
Example 2:
PRACTICE PROBLEMS
,Change the following percentages to fractions and reduce to lowest terms.
9. 1% ________________
10. 2% ________________
11. 50% ________________
12. 80% ________________
13. 3% ________________
Answers on p. 587
To change a percentage to a decimal, drop the percent sign, and move the decimal point two places to the left
(add zeros as needed).
Example 1:
Example 2:
Example 3:
Note
Example 3 is an alternative method. Drop the percent sign. Write the remaining number as the numerator.
Write “100” as the denominator. Reduce the result to lowest terms. Divide the numerator by the
denominator to obtain a decimal.
PRACTICE PROBLEMS
Change the following percentages to decimals.
14. 10% ________________
15. 35% ________________
16. 30% ________________
17. 14.2% ________________
18. ¼% ________________
Answers on p. 587
To change a percentage to a ratio, change it to a fraction and reduce to lowest terms, then place the numerator
as the first term of the ratio and the denominator as the second term. Separate the two terms with a colon (:).
Example:
, PRACTICE PROBLEMS
Change each of the following percentages to a ratio. Express in lowest terms:
19. 25% ________________
20. 11% ________________
21. 75% ________________
22. 4.5% ________________
23. ⅖% ________________
Answers on p. 587
From: Gray Morris: Calculate with Confidence, 4th ed.
HOUSEHOLD SYSTEM
HOUSEHOLD SYSTEM
The household system is an old system and the least accurate of the three systems of measure. It is a
modified system designed for everyday use at home. Nurses need to be familiar with household measures,
because clients often use utensils in the home to take prescribed medications. Capacities of utensils such as a
teaspoon, a tablespoon, and a cup vary from one house to another; therefore liquid measures are approximate.
Because of the increase in nursing care provided at home (home care, visiting nurse), it is imperative that
nurses become adept in converting from one system to another. When calculating doses or interpreting the
health care provider's instructions for the client at home, the nurse must remember that household measures
are used. Consequently the nurse must be able to calculate equivalents for adaptation in the home, even
though medication administration spoons, droppers, and medication measuring cups (Figure 7-3) are
available.
FIGURE 7-3 Medicine cup showing household/metric measurements.
Using household measures for dosage measurements can place a client at risk. Always advise clients and their
families to use the measuring devices or droppers packaged with the medication or provided by the pharmacy.
Common household measures to memorize are the following:
1 teaspoon (t, tsp) = 5 mL
1 tablespoon (T, tbs) = 15 mL
1 measuring cup = 8 oz
Note
Anything less than a teaspoon should be measured in a syringe-type device that has no needle and not a
measuring cup. Use the measuring devices packaged with the medication or provided by the pharmacy.
