Math: Basic Tutorials : Decimals

Decimals

Decimals play a crucial role in healthcare calculations. Decimal notation represents numbers in base-10, with each digit’s position indicating a specific power of 10. Understanding decimal notation is key to working with smaller quantities and ensuring accuracy in client care.

This section will cover decimal notation, rounding techniques, and converting between fractions and decimals. You'll also learn how to perform arithmetic operations—addition, subtraction, multiplication, and division—using decimals. Through clear examples, this section will help you confidently apply decimal calculations in real-world healthcare scenarios.

Decimals

Decimal Notation

The decimal point is a crucial marker in the place value system, separating whole numbers from fractional values. Digits to the left represent whole numbers, while those to the right indicate fractional parts such as tenths , hundredths, and so on.

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Click on the titles below to view each example.

Example 1

Example 1:
Name the following numbers:
$203.65$	Solution:	Two hundred three and sixty-five hundredths
$2.008$	Solution:	Two and eight thousandths

Example 2

Example 2:
Write out the following numbers:
One thousand twenty-two and three tenths	Solution:	$1022.3$
Eighty thousand and eighty thousandths	Solution:	$80,000.080$

Converting between Fractions & Decimals

The decimal place value determines how to convert a decimal into a fraction. To convert a decimal to a fraction, write the decimal as a numerator over a denominator based on its place value, then simplify if needed.

Example:
This number ends at the thousandths place value. Therefore you put the number over 1000. Then simplify the fraction.	$0.045 = \frac{45}{1000}$
Solution:	$= \frac{9}{20}$

Example:

This number ends at the thousandths place value. Therefore you put the number over 1000.

Then simplify the fraction.

$0.045 = \frac{45}{1000}$

Solution:

$= \frac{9}{20}$

Rounding Decimal Notation

To round to a certain place:

Locate the digit in that place.
Consider the next digit to the right.
If the digit to the right is 5 or greater, round up; if the digit to the right is 4 or lower, keep digit the same.

number 123.456 with places labelled. 1=hundred, 2=ten, 3=hundred, 4=tenth, 5=hundredth, 6=thousandth

Click on the titles below to view each example.

Example 1

Example 1:
Round $0.084$ to the nearest tenth.
Locate the digit in the tenths place.	$0. 084$
Consider the next digit to the right, 8 Since 8 is greater than or equal to 5, round up.	$0. 08 = 0. 1$
Solution:	$0.1$

Example 2

Example 2:
Round $212.5604$ to the nearest hundredth.
Locate the digit in the hundredths place.	$212.5 604$
Consider the next digit to the right, 0 Since 0 is lower than 4, keep the digit the same.	$212.5 604 = 212.5 6$
Solution:	$212.56$

Decimal Arithmetic Operations

Arithmetic operations—addition, subtraction, multiplication, and division—are essential for the calculations you’ll encounter daily. Learning to apply these operations with decimals ensures accurate results and precise measurements.

Click on the titles below to view each example.

Example 1

Example 1:
A client receives the following doses of medication every day: 0.2 mg, 1.05 mg and 2.84 mg. What is the total daily dosage?
The total daily dosage is the sum of the individual dosages.	$0.2 + 1.05 + 2.84 = 4.09$
Solution:	The total daily dosage is 4.09mg

Example 2

Example 2:
A patient's temperature reading in the morning was 102.3°F. In the afternoon, their temperature was 98.5°F. What is the decrease in temperature?
We have to subtract the afternoon temperature from the morning temperature. Temp decrease = morning − afternoon	$102.3 - 98.5 = 3.8$
Solution:	The temperature decrease was 3.8°F

Example 2:

A patient's temperature reading in the morning was 102.3°F. In the afternoon, their temperature was 98.5°F. What is the decrease in temperature?

We have to subtract the afternoon temperature from the morning temperature.

Temp decrease = morning − afternoon

$102.3 - 98.5 = 3.8$

Solution:

The temperature decrease was 3.8°F

Example 3

Example 3:
A patient weighs 80.4 kg. One kg is 2.2 lbs. What is the patient's weight in pounds?
We need to multiply 80.4 kg by 2.2 lbs to find the weight in pounds.	$80.4 \times 2.2 = 176.88$
Solution:	The patient weighs 176.88 lbs.

Example 4

Example 4:
A nurse is pouring servings of juice from a pitcher with 1050 mL of juice. How many 150 mL servings can they pour?
For long division, you need to divide the whole (1050 mL) by the part (150 mL).	$150 ⟌ 1050 = 7$
Solution:	The nurse can pour 7 servings of juice.

Practice

Additional Resources

Learning Portal Basic Tutorials: Decimals & Percent

Last Updated: Jun 25, 2025 4:00 PM
URL: https://tlp-lpa.ca/math-tutorials
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Math: Basic Tutorials : Decimals

Decimals

Decimals

Decimal Notation

Converting between Fractions & Decimals

Rounding Decimal Notation

Decimal Arithmetic Operations

Practice

Additional Resources