Working with Decimals
Working with Decimals: Expanding Your Math Skills
This chapter delves into the world of decimals, a crucial concept for various applications, particularly in healthcare settings. You’ll explore decimal place value, operations with decimals, conversions between fractions and decimals, and realworld examples relevant to healthcare.
Understanding Decimal Place Value and Notation
Decimals extend our number system beyond whole numbers. They represent parts of a whole, using a decimal point (.) to separate the whole number part from the fractional part. Each digit to the right of the decimal point has a specific place value based on its position.
 Tenths (0.1): The first digit to the right of the decimal point represents tenths.
 Hundredths (0.01): The second digit to the right of the decimal point represents hundredths.
 Thousandths (0.001): The third digit to the right of the decimal point represents thousandths, and so on.
Reading and Writing Decimals:
Read decimals by stating the whole number part, followed by “and” and then reading each digit to the right of the decimal point by its place value (tenths, hundredths, etc.).

 Example: 3.14 can be read as “three and fourteen hundredths.”
Write decimals by placing the whole number to the left of the decimal point and the fractional part to the right. If a whole number part is missing (zero), include a 0 before the decimal point.

 Example: Seven hundredths can be written as 0.07.
Comparing Decimals:
Line up the decimals by adding zeros to the right if necessary.
Compare the digits from left to right, starting with the whole number part.

 The larger whole number part indicates a larger decimal.
 If the whole number parts are the same, compare the digits to the right of the decimal point. The first digit that is different determines the larger decimal. The larger digit corresponds to the larger decimal.
Practice Problems:
 Write the following decimal in words: 2.59 (Two and fiftynine hundredths)
 Write the following decimal: Seven and eight tenths (7.8)
 Arrange the following decimals from least to greatest: 1.23, 1.3, 1.19 (1.19, 1.23, 1.3)
Adding, Subtracting, Multiplying, and Dividing Decimals
Similar to whole numbers, we can perform addition, subtraction, multiplication, and division with decimals. The key lies in aligning the decimals correctly.
 Aligning Decimals: When adding, subtracting, or multiplying decimals, line up the decimal points in all the numbers involved. Add or remove zeros to the right as needed to ensure proper alignment.
 Decimal Point in the Answer: The decimal point in the answer will depend on the operation performed.
Addition and Subtraction:
Decimals are added or subtracted like whole numbers, considering the decimal point alignment.

 Example: 2.35 + 1.7 = 4.05 (align decimals, add digits in each place value column)
Multiplication:
The number of decimal places in the product is the sum of the number of decimal places in each factor (number being multiplied).

 Example: 2.5 x 3.1 = 7.75 (2 decimal places + 1 decimal place = 3 decimal places in the product)
Division:
Dividing by a decimal is the same as dividing by a whole number if we convert the decimal divisor to a fraction with a denominator of 10 (add zeros), 100 (add two zeros), etc., depending on the number of decimal places in the divisor.

 Example: 12.4 ÷ 0.2 = 12.4 ÷ (2/10) = 12.4 x (5) = 62 (convert 0.2 to 2/10, then multiply by the reciprocal 5/1)
Practice Problems:
 Solve: 4.72 + 1.89 = ( )
 Solve: 15.4 – 8.21 = ( )
 Solve: 3.2 x 0.75 = ( )
 Solve: 18.6 ÷ 0.3 = ( ) (convert 0.3 to a fraction with a denominator of 10)
Converting Between Fractions and Decimals
There’s a close relationship between fractions and decimals. We can convert between them using various methods.
Fraction to Decimal:
 Divide the numerator (top number) by the denominator (bottom number) using
 Divide the numerator (top number) by the denominator (bottom number) using long division or a calculator. If the division terminates (ends with a remainder of 0), you get an exact decimal representation. If the division doesn’t terminate (repeating decimals), you can round to a desired number of decimal places.
Decimal to Fraction:
 The decimal represents a fraction with a denominator of 10 (if one decimal place), 100 (if two decimal places), and so on (depending on the number of decimal places).
 Example: 0.75 can be written as 75/100 (75 hundredths) which can be simplified to 3/4.
Practice Problems:
 Convert the following fraction to a decimal: 3/8 (Divide 3 by 8 using a calculator and round to two decimal places: 0.37)
 Convert the following decimal to a fraction: 0.625 (Write as 625/1000 and simplify to 5/8)
Applications of Decimals in Healthcare Settings
Decimals play a crucial role in various healthcare settings. Here are some examples:
 Medication Dosages:
Medications are often prescribed in precise decimal amounts (e.g., 2.5 mg of medication). Accurate measurement and administration of these dosages are essential for patient safety.

Vital Signs:
Body temperature, blood pressure, and other vital signs are often recorded using decimals (e.g., 37.2°C temperature, 120/80 mmHg blood pressure). Understanding decimal place values is crucial for interpreting these measurements.
 Laboratory Results:
Blood sugar levels, cholesterol levels, and other laboratory results are often reported in decimal format. Healthcare professionals need to be able to interpret these values and make informed decisions based on them.
By mastering decimal operations and conversions, you’ll be wellequipped to handle calculations and measurements in healthcare settings, ensuring patient safety and effective treatment.
This chapter has comprehensively covered decimal place value, operations, conversions, and applications in healthcare. Remember, consistent practice and a strong foundation in decimals will empower you to excel in your healthcare endeavors.