Learn the numbers
behind better care.

Number

A number is a mathematical value used to count, measure, order, label, or calculate quantities.

Clinical example: A nurse records that 24 patients attended a diabetes education session; 24 is the number of patients.

Natural number

A natural number is a positive counting number, usually beginning with 1.

Clinical example: If a ward has 18 occupied beds, 18 is a natural number because it counts beds.

Whole number

A whole number is a non-negative integer: 0, 1, 2, 3, and so on.

Clinical example: A unit may report 0 patient falls during a shift; 0 is a whole number.

Integer

An integer is a whole number that may be negative, positive, or zero and has no fractional part.

Clinical example: If a temperature change is recorded as −2°C, the value −2 is an integer.

Positive number

A positive number is a number greater than zero.

Clinical example: A patient gains 2 kg during nutritional rehabilitation; +2 is a positive change.

Negative number

A negative number is a number less than zero.

Clinical example: A patient's fluid balance is −350 mL, meaning output exceeded intake by 350 mL.

Zero

Zero is the number that represents no quantity and separates positive numbers from negative numbers.

Clinical example: A ward reports zero medication-administration errors during the audit period.

Even number

An even number is an integer that is exactly divisible by 2.

Where: n = an even integer; k = any integer

Clinical example: A nurse educator divides 20 students into two equal groups of 10; 20 is even.

Odd number

An odd number is an integer that is not exactly divisible by 2.

Where: n = an odd integer; k = any integer

Clinical example: If 21 patients are enrolled in a study, 21 is an odd number.

Prime number

A prime number is an integer greater than 1 with exactly two positive factors: 1 and itself.

Clinical example: If 17 nurses are selected for a pilot activity, 17 is a prime number because its only positive factors are 1 and 17.

Composite number

A composite number is an integer greater than 1 that has more than two positive factors.

Clinical example: If 18 nurses attend a workshop, 18 is composite because it is divisible by 2, 3, 6, and 9 as well as 1 and 18.

Real number

A real number is any number that can be represented on the number line, including rational and irrational numbers.

Clinical example: A patient's body temperature of 37.2°C is represented by a real number.

Rational number

A rational number is a number that can be written as a fraction of two integers with a nonzero denominator.

Where: a = integer numerator; b = nonzero integer denominator

Clinical example: A medication dose of 0.5 tablet is rational because 0.5 can be written as 1/2.

Irrational number

An irrational number is a real number that cannot be expressed exactly as a ratio of two integers.

Clinical example: When a circular wound area is estimated using π, the number π is irrational.

Absolute value

The absolute value of a real number is its distance from zero on the number line, regardless of direction.

Where: x = the number; |x| = its non-negative distance from zero

Clinical example: A fluid-balance change of −400 mL has an absolute value of 400 mL when only the magnitude of the difference is considered.

Numerator

The numerator is the number written above the fraction bar and indicates how many parts are being considered.

Where: a = numerator; b = denominator

Clinical example: If 18 of 60 patients developed nausea, the fraction is 18/60 and 18 is the numerator.

Denominator

The denominator is the number written below the fraction bar and indicates the total number of equal parts or reference units.

Where: a = numerator; b = denominator

Clinical example: If 18 of 60 patients developed nausea, 60 is the denominator because 60 patients were observed.

Fraction

A fraction represents one quantity as a part of another and is written as a numerator divided by a denominator.

Where: a = numerator; b = denominator

Clinical example: If 15 of 20 nurses completed training, the fraction completing training is 15/20.

Proper fraction

A proper fraction is a positive fraction whose numerator is smaller than its denominator, so its value is less than 1.

Clinical example: If 3 of 8 patients require additional teaching, 3/8 is a proper fraction.

Improper fraction

An improper fraction is a positive fraction whose numerator is greater than or equal to its denominator, so its value is at least 1.

Clinical example: If a calculation gives 9/4 hours of total nursing time per patient, 9/4 is an improper fraction equal to 2.25 hours.

Mixed number

A mixed number combines a whole number and a proper fraction to represent a value greater than 1.

Clinical example: A dressing procedure lasting 2 1/2 minutes is written as a mixed number.

Decimal

A decimal is a way of representing numbers using place values separated by a decimal point.

Clinical example: A patient's serum potassium level may be recorded as 4.2 mmol/L; 4.2 is a decimal number.

Decimal place

A decimal place is the position of a digit to the right of the decimal point.

Clinical example: A temperature of 37.26°C has two decimal places; if reported as 37.3°C, it has one decimal place.

Rounding

Rounding is the process of replacing a number with a nearby value having fewer digits while preserving an appropriate level of accuracy.

Clinical example: A mean pulse rate of 82.47 beats/min may be reported as 82.5 beats/min when one decimal place is appropriate.

Significant figure

A significant figure is a digit in a number that contributes to the reported precision of that number.

Clinical example: A laboratory value reported as 0.00456 has three significant figures: 4, 5, and 6.

Scientific notation

Scientific notation expresses a number as a coefficient multiplied by a power of 10.

Where: a = coefficient; n = integer exponent

Clinical example: A bacterial count of 2,500,000 CFU can be written as 2.5 × 10^6 CFU.

Addition

Addition is the arithmetic operation of combining two or more quantities to obtain their total.

Where: a and b = quantities being added

Clinical example: If 12 patients were admitted in the morning and 8 in the evening, the total admissions are 12 + 8 = 20.

Subtraction

Subtraction is the arithmetic operation of finding how much remains or the difference between two quantities.

Where: a = starting quantity; b = quantity removed or compared

Clinical example: If a ward had 30 patients and 7 were discharged, 30 − 7 = 23 patients remain.

Multiplication

Multiplication is the arithmetic operation of combining equal groups or scaling one quantity by another.

Where: a and b = factors being multiplied

Clinical example: If 6 nurses each assess 5 patients, they assess 6 × 5 = 30 patients in total.

Division

Division is the arithmetic operation of separating a quantity into equal parts or determining how many times one quantity is contained in another.

Where: a = dividend; b = divisor; a/b = quotient

Clinical example: If 24 patients are assigned equally to 4 nurses, each nurse receives 24 ÷ 4 = 6 patients.

Sum

A sum is the result obtained by adding two or more quantities.

Where: Σ = add all indicated values; x_i = each value; n = number of values

Clinical example: The pain scores 3, 4, and 5 have a sum of 12.

Difference

A difference is the result obtained when one quantity is subtracted from another.

Where: a and b = the two quantities being compared

Clinical example: If mean knowledge score rises from 14 to 19 after teaching, the difference is 19 − 14 = 5 points.

Product

A product is the result obtained by multiplying two or more quantities.

Where: a and b = factors; a×b = product

Clinical example: If 8 nurses each complete 3 observations, the product 8 × 3 gives 24 observations.

Quotient

A quotient is the result obtained by dividing one quantity by another.

Where: a = dividend; b = divisor; a/b = quotient

Clinical example: Dividing 36 patients among 6 nurses gives a quotient of 6 patients per nurse.

Order of operations

The order of operations is the agreed sequence used to evaluate mathematical expressions consistently.

Clinical example: When calculating 2 + 3 × 4 for a staffing exercise, multiplication is done first, giving 2 + 12 = 14 rather than 20.

Bracket

A bracket is a grouping symbol used to indicate that the enclosed part of an expression should be treated together.

Clinical example: In 5 × (2 + 3) dressing packs, the bracketed 2 + 3 is calculated first, giving 25 packs.

Parenthesis

A parenthesis is a curved grouping symbol, written ( ), used to group part of a mathematical expression.

Clinical example: In (post-test score − pre-test score), parentheses show that the score difference is treated as one quantity.

Power

A power is an expression showing repeated multiplication of a base by itself a specified number of times.

Where: a = base; n = exponent

Clinical example: If a square wound area is estimated from a side length of 4 cm, 4² = 16 cm² uses a power.

Exponent

An exponent is the number or symbol that indicates how many times a base is used as a factor in a power.

Where: a = base; n = exponent

Clinical example: In 10³ = 1000, the exponent 3 means 10 × 10 × 10.

Square

The square of a number is the result of multiplying that number by itself.

Where: x = original number; x² = square of x

Clinical example: A square pressure-ulcer image measuring 3 cm on each side has an area of 3² = 9 cm².

Cube

The cube of a number is the result of multiplying that number by itself three times.

Where: x = original number; x³ = cube of x

Clinical example: A cubic container with side length 2 cm has a volume of 2³ = 8 cm³.

Square root

The square root of a non-negative number is a value that, when multiplied by itself, gives the original number.

Where: x = original non-negative number; y = square root

Clinical example: If a square wound has an area of 25 cm², its side length is √25 = 5 cm.

Cube root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Where: x = original number; y = cube root

Clinical example: If a cubic teaching model has a volume of 64 cm³, each equal side is ∛64 = 4 cm.

Reciprocal

The reciprocal of a nonzero number is 1 divided by that number, producing a value whose product with the original number is 1.

Where: x = original nonzero value; 1/x = reciprocal

Clinical example: The reciprocal of 4 is 1/4; this idea is used when rates or transformed values are inverted.

Factor

A factor is a number or algebraic quantity that multiplies with another quantity to produce a product.

Clinical example: Because 4 × 6 = 24, both 4 and 6 are factors of 24 patient observations.

Multiple

A multiple of a number is a value obtained by multiplying that number by an integer.

Clinical example: If observations are scheduled every 4 hours, 8, 12, and 16 hours are multiples of 4.

Ratio

A ratio compares the magnitude of one quantity with another by division.

Where: a = first quantity; b = second quantity

Clinical example: If a ward has 10 nurses and 30 patients, the nurse-to-patient ratio is 10:30, which simplifies to 1:3.

Proportion

A proportion is a ratio in which the numerator is part of the denominator, or an equation stating that two ratios are equal, depending on context.

Where: x = number with the characteristic; n = total number; p = proportion

Clinical example: If 24 of 60 nursing students pass a skills test, the proportion passing is 24/60 = 0.40.

Percentage

A percentage is a proportion expressed per 100.

Where: part = number of interest; whole = total number

Clinical example: If 48 of 60 nurses complete hand-hygiene training, the completion percentage is 48/60 × 100 = 80%.

Percent change

Percent change expresses the difference between a new value and an original value as a percentage of the original value.

Where: new = later value; original = starting value

Clinical example: If medication errors fall from 20 to 15 per month, the percent change is (15 − 20)/20 × 100 = −25%, a 25% decrease.

Rate

A rate is a ratio that describes how frequently an event or quantity occurs relative to another quantity, often including time in the denominator.

Where: numerator = events/quantity; denominator = exposure or time; k = optional scaling constant

Clinical example: If 6 patient falls occur during 1,200 patient-days, the fall rate is 6 per 1,200 patient-days, often rescaled for reporting.

Unit rate

A unit rate is a rate expressed for one unit of the denominator.

Where: quantity = total amount; unit = one unit of time, person, or other denominator

Clinical example: If 120 mL of intravenous fluid runs over 4 hours, the unit rate is 30 mL per hour.

Equivalent ratio

Equivalent ratios are ratios that express the same proportional relationship even though their numbers are different.

Where: a:b = original ratio; k = common nonzero scaling factor

Clinical example: A nurse-to-patient ratio of 1:4 is equivalent to 5:20 because multiplying both parts by 5 preserves the same staffing relationship.

Unit conversion

Unit conversion changes a measurement from one unit to another equivalent unit without changing the underlying quantity.

Where: conversion factor = ratio equal to 1 that links the two units

Clinical example: A prescribed fluid amount of 1.5 L can be converted to 1500 mL.

Dimensional analysis

Dimensional analysis is a method of calculation that uses units and conversion factors so unwanted units cancel and the desired unit remains.

Where: given quantity = starting measurement; conversion factor = equivalent ratio; units cancel algebraically

Clinical example: To convert 0.75 g to mg, a nurse calculates 0.75 g × 1000 mg/1 g = 750 mg; the g units cancel.

Cross multiplication

Cross multiplication is a method for solving an equation containing two equal ratios by multiplying each numerator by the opposite denominator.

Where: a,b,c,d = quantities in two equivalent ratios; denominators must be nonzero

Clinical example: If 2 tablets contain 500 mg, then x tablets contain 750 mg: 2/500 = x/750, so 500x = 1500 and x = 3.

Variable

A variable in algebra is a symbol that represents a quantity whose value may change or may be unknown.

Clinical example: If x represents the number of patients assigned to each nurse, x changes when staffing or patient numbers change.

Constant

A constant is a fixed value that does not change within a particular mathematical expression or problem.

Clinical example: In the formula °F = 1.8°C + 32, the numbers 1.8 and 32 are constants.

Coefficient

A coefficient is a numerical or symbolic factor that multiplies a variable or another algebraic term.

Where: a = coefficient; x = variable

Clinical example: In y = 2x + 5, the coefficient of x is 2.

Term

A term is a single number, variable, or product of numbers and variables within an algebraic expression.

Clinical example: In 3x + 5, the expression has two terms: 3x and 5.

Expression

An expression is a mathematical combination of numbers, variables, and operations that does not state an equality or inequality.

Clinical example: If x is the number of patients, 2x + 5 is an expression that could represent total observations required.

Equation

An equation is a mathematical statement asserting that two expressions are equal.

Where: Both sides represent equal quantities

Clinical example: If four nurses share 24 patients equally, the equation 4x = 24 gives x = 6 patients per nurse.

Equality

Equality is the mathematical relationship indicating that two quantities or expressions have the same value.

Where: a and b = quantities with the same value

Clinical example: The statement 500 mg = 0.5 g is an equality because the two quantities represent the same dose.

Inequality

An inequality is a mathematical statement comparing two quantities using symbols such as <, >, ≤, or ≥ rather than stating exact equality.

Where: < = less than; > = greater than; ≤ = less than or equal to; ≥ = greater than or equal to

Clinical example: A hospital protocol may state that oxygen saturation should be ≥94% for a particular patient group.

Substitution

Substitution is the process of replacing a variable in an expression or formula with a known value.

Clinical example: If total nursing time is T = 20x minutes and x = 6 patients, substituting 6 gives T = 120 minutes.

Rearranging a formula

Rearranging a formula means applying equivalent algebraic operations to isolate a different variable while preserving the equality.

Clinical example: From BMI = weight/height², a researcher can rearrange to weight = BMI × height² when weight is the unknown quantity.

Linear equation

A linear equation is an equation in which variables appear only to the first power and its graph is a straight line in two dimensions.

Where: x = independent quantity; y = dependent quantity; m = slope; b = intercept

Clinical example: If estimated documentation time is y = 5x + 10 minutes for x patients, each additional patient adds 5 minutes.

Slope

Slope is the change in a dependent quantity divided by the corresponding change in an independent quantity along a straight line.

Where: m = slope; x1,x2 = two x-values; y1,y2 = corresponding y-values

Clinical example: If documentation time rises from 30 to 40 minutes when patient count rises from 4 to 6, the slope is (40−30)/(6−4)=5 minutes per patient.

Intercept

The intercept in a linear equation is the value of the dependent quantity when the independent quantity equals zero.

Where: b = y-intercept; m = slope; x,y = a point on the line

Clinical example: In y = 5x + 10, the intercept 10 represents the predicted baseline time when x = 0.

Coordinate

A coordinate is a numerical value used to specify the position of a point relative to an axis or reference system.

Clinical example: On a graph of study hours and test score, x = 4 and y = 72 locate a student's observation.

Cartesian plane

The Cartesian plane is a two-dimensional coordinate system formed by perpendicular horizontal and vertical axes, usually called the x-axis and y-axis.

Clinical example: A nurse researcher plots hours of clinical practice on the x-axis and competency score on the y-axis.

Ordered pair

An ordered pair is a pair of values written in a fixed order, usually (x, y), that identifies a point on the Cartesian plane.

Where: x = horizontal coordinate; y = vertical coordinate

Clinical example: The point (6, 85) may represent 6 hours of practice and an 85-point competency score.

Function

A function is a mathematical relationship that assigns each permitted input exactly one output.

Where: x = input; f = rule; y = output

Clinical example: If y = 2x + 5 gives estimated documentation time from patient count x, each patient count has one corresponding predicted time.

Independent quantity

An independent quantity is the input quantity whose value is chosen, observed, or allowed to vary when describing a mathematical relationship.

Clinical example: When plotting training hours against competency score, training hours can be treated as the independent quantity on the x-axis.

Dependent quantity

A dependent quantity is the output quantity whose value is determined by or described in relation to an independent quantity.

Clinical example: If a function predicts competency score from training hours, predicted competency score is the dependent quantity.

Logarithm

A logarithm is the exponent to which a specified base must be raised to produce a given positive number.

Where: b = positive base not equal to 1; x = positive number; y = logarithm

Clinical example: Because 10² = 100, log₁₀(100) = 2; logarithms are often used when healthcare measurements span very wide ranges.

Natural logarithm

The natural logarithm is a logarithm with base e, where e is approximately 2.71828.

Where: e ≈ 2.71828; x must be positive

Clinical example: In logistic regression, the natural logarithm of the odds is modelled as a linear combination of predictors.

Base-10 logarithm

A base-10 logarithm is a logarithm with base 10 and is commonly written log10 or log when the base is understood.

Where: x = positive number; base = 10

Clinical example: If a microbial count is 1000, log₁₀(1000) = 3 because 10³ = 1000.

Exponential function

An exponential function is a function in which the variable appears in the exponent and the base is a positive constant not equal to 1.

Where: a = starting scale; b = positive base not equal to 1; x = input; y = output

Clinical example: A model of bacterial growth may use an exponential function when the population increases by a similar proportion during equal time intervals.

Log transformation

A log transformation replaces each positive observation with its logarithm, often to reduce right-skewness or make multiplicative relationships easier to model.

Where: x = original positive value; x* = transformed value

Clinical example: Highly right-skewed hospital-cost data may be analysed after taking the logarithm of each positive cost value.

Square-root transformation

A square-root transformation replaces each non-negative observation with its square root, often to reduce moderate right-skewness or stabilize variability in count-like data.

Where: x = original non-negative value; x* = transformed value

Clinical example: If infection counts across wards are right-skewed, a researcher may examine the square root of each count before using a method that needs more stable variability.

Reciprocal transformation

A reciprocal transformation replaces each nonzero observation with its reciprocal, 1 divided by the original value.

Where: x = original nonzero value; x* = reciprocal-transformed value

Clinical example: A researcher may explore 1/x for a highly skewed positive time variable, but must interpret the transformed scale carefully.

Place value

Place value is the value a digit has because of its position within a number.

Clinical example: In a temperature of 37.25°C, the 2 is in the tenths place and the 5 is in the hundredths place.

Remainder

A remainder is the amount left over when one integer is divided by another and the division is not exact.

Where: a = dividend; b = nonzero divisor; q = integer quotient; r = remainder

Clinical example: If 25 patients are divided among 4 nurses, each can be assigned 6 patients with 1 patient remaining for redistribution.

Summation notation

Summation notation uses the Greek capital letter sigma, Σ, to represent the addition of a sequence of values.

Where: Σ = sum; i = index; x_i = each observation; n = number of observations

Clinical example: For pain scores 3, 4, and 5, Σx = 3 + 4 + 5 = 12.

Conversion factor

A conversion factor is a ratio of equivalent quantities in different units and therefore has a numerical value of 1 as a unit relationship.

Where: Numerator and denominator represent the same physical quantity in different units

Clinical example: Because 1 g = 1000 mg, the factor 1000 mg/1 g converts grams to milligrams while representing the same quantity.

Absolute change

Absolute change is the arithmetic difference between a new value and an original value, expressed in the original measurement unit.

Where: new = later value; original = starting value

Clinical example: If the mean knowledge score increases from 14 to 19, the absolute change is 19 − 14 = 5 points.

Relative change

Relative change is the absolute change divided by the original value, expressing the change relative to where the measurement started.

Where: new = later value; original = starting value

Clinical example: If falls decrease from 20 to 15, the relative change is (15−20)/20 = −0.25, representing a 25% decrease.

Percentage point

A percentage point is the arithmetic difference between two percentages.

Where: p1 = original percentage; p2 = later percentage

Clinical example: If hand-hygiene compliance rises from 60% to 75%, it increases by 15 percentage points, although the relative percent increase is 25%.

Base

A base is the number that is repeatedly multiplied in a power and is also the fixed reference number used in a logarithm.

Where: b = base; x = exponent

Clinical example: In scientific notation such as 2.5 × 10⁶, the power uses base 10.