Decimals

1Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

Gray Morris

2Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

Unit One: Chapter 3

3Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

1. Read decimals2. Write decimals3. Compare the size of

decimals to one another

4. Convert fractions to decimals

5. Convert decimals to fractions

6. Add decimals7. Subtract decimals8. Multiply decimals9. Divide decimals10. Round decimals to

nearest tenth11. Round decimals to

nearest hundredth

After reviewing this chapter, you should be able to:


Dosages and other measurements in health care

Understanding is crucial Decimal points—major source of

medication errors Write with great care!

Examples: Digoxin 0.125 mgCoreg 3.125 mg


A decimal is a fraction with a denominator that is a multiple of 10. The decimal (.) is used to indicate place value.Examples:

Caution: each decimal expression with a value less than 1 is preceded by a leading zero to emphasize the presence of a decimal, according to national patient safety standards (ISMP and TJC)

3 equals 0.3 stated as "three tenths"

1018

equals 0.18 stated as "eighteen hundredths"100



Reading1. Read the whole number on the left2. Read the decimal point as the word “and”3. Read the decimal fraction on the rightExample: 8.3 = “eight and three tenths”

4.06 = “four and six hundreths” 0.5 = “five tenths

Safety Point: In emergencies, when reading an order back to a health care provider, read the zero aloud. 0.5 becomes “zero point five”


Write as follows1. The whole number (if none, then write a zero -

“0”)2. The decimal point to indicate the place of value3. The decimal fraction portion of the number

Examples: “seven and five tenths” = 7.5“one hundred twenty-five thousandths” = 0.125

Safety Point: Unnecessary or “trailing” zeros should NOT be placed at end of numbers (ISMP and TJC “Do Not Use” list from 2005). Trailing zeros are acceptable only to demonstrate the precision of value in lab results or imaging studies or the sizes of lesions or tubes.


Zeros do not change the value of the number whether added at the beginning or the end, but they are unsafe as trailers. Examples: .7 is the same numerical value as

0.7 12.6250 is the same value as

12.625 30.0 can be misinterpreted as

300! USE leading zeros; AVOID trailing zeros


Zeros added within a decimal number change the value dramatically

Example: 0.375 mg is NOT the same as 0.0375 mg

2.025 mg is NOT the same as 20.025 mg


Different whole numbers If whole numbers are present and different,

whole numbers are compared to determine largest

Example: 4.8 is greater than 2.9

Same or no whole number The number in the tenths place determines

largest Example: 0.45 is larger than 0.37


Same or no whole number, and the number in the tenths place is the same

The decimal with the highest number in the hundredths place is the largest

Examples: 0.67 is larger than 0.66 0.17 is larger than 0.14 0.09 is larger than 0.08


Place the numbers in the columns so the decimals are lined up. Add or subtract from left to right. Examples:

16.421.813.0

51.2Safety Point: Zeros may be added to help line up decimals – don’t include in final answer!

18.62.6

1616.0

0.7000.7502.324

3.774


Place decimal correctly! Multiply numbers; in the product

(answer), count decimal places right to left equal to the total decimal places in the numbers being multiplied. Example: 1.2

3.2 24 36 384. = 3.84

x


Add zeros where needed to ensure correct placement of decimal in answer Example:

0.110.33

33 33

0363. = 0.0363

x


Multiplying by 10, 100, 1,000 can be done by moving decimal to the right one space for each zero in the number by which multiplying Example: 1.6 x 10 = 1.6 = 16

5.2 x 100 = 5.20 = 520


Same as for whole numbers

Example: = 27 divided by 9

QuotientDivisor Dividend

9 27


To divide by a whole number, place decimal in quotient directly above decimal in dividend

3.55 17.5

- 15 25- 25

0


. 0.3 6.96

Move the decimal in the divisor to the right until the number is a whole number. Then move the decimal in the dividend the same number of spaces.23.2

3 69.6

- 6 9- 9

6

-6

0


To divide by 10, 100, or 1,000, move decimal to the left one place for each zero in the divisor

Examples: 00.46 10 = 0.046

000.07 100 = 0.0007


Based on equipment Most carry to hundredths place and rounds to

tenths If number in hundredths place is 5 or

greater, add 1 to tenths place and drop the hundredths Example: 4.15 rounds to 4.2


If number in hundredths place is less than 5, drop number to the right of tenths place Example: and 4.14 rounds to 4.1

To express numbers in hundredths, carry equations out to thousandths and then round


Rewrite fraction in division format Divide the numerator by the denominator

and add zeros as needed Method can be used to compare fraction

size

0.425 2.0

5

1 1

0.333... and 0.166...3 6

1 1 is larger than 3 6

Therefore


Write decimal as a whole number in numerator of fraction, express denominator as powers of 10

Place the number 1 in denominator of fraction and add as many zeros as there are places to right of decimal Example: 0.4 is read as “four tenths” = 4/10 =

2/5 0.65 is read as “sixty-five

hundredths = 65/100 = 13/20 reduced

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Decimals