🔢 R Numbers & Math – Perform Arithmetic and Numeric Operations in R

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🧲 Introduction – Numbers and Math in R Programming

R is fundamentally a numeric computing language, built to handle everything from simple arithmetic to complex statistical modeling. Understanding how R treats numbers and performs mathematical operations is essential for any data analysis or machine learning task.

🎯 In this guide, you’ll learn:

• How numbers are represented in R
• Arithmetic, relational, and mathematical functions
• How to work with integers, decimals, and special values
• Practical math operations including rounding, exponentials, and trigonometry

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🔤 Types of Numbers in R

Type	Example	Description
numeric	3.14	Default type for real numbers
integer	42L	Whole numbers, declared with L
complex	2+3i	Real + imaginary numbers
double	5.5	Subtype of numeric (64-bit float)

a <- 10      # numeric
b <- 5L      # integer
c <- 2 + 3i  # complex

Use class() and typeof() to inspect:

class(a)     # "numeric"
typeof(b)    # "integer"
is.complex(c) # TRUE

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➕ Basic Arithmetic Operators

Operator	Operation	Example
+	Addition	x + y
-	Subtraction	x - y
*	Multiplication	x * y
/	Division	x / y
%%	Modulo (remainder)	x %% y
%/%	Integer division	x %/% y
^ or **	Exponentiation	x ^ y

x <- 15
y <- 4

x + y     # 19
x %% y    # 3
x %/% y   # 3
x ^ 2     # 225

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📐 Built-in Math Functions

R provides a rich set of built-in math functions.

Function	Description	Example
abs(x)	Absolute value	abs(-5) = 5
sqrt(x)	Square root	sqrt(16) = 4
log(x)	Natural log (base e)	log(10)
log10(x)	Base-10 log	log10(100)
exp(x)	Exponential	exp(2)
round(x)	Round to nearest integer	round(3.65)
ceiling(x)	Round up	ceiling(4.1)
floor(x)	Round down	floor(4.9)
sign(x)	Sign of number (-1, 0, 1)	sign(-10)

✅ Example:

x <- -3.5
abs(x)        # 3.5
round(x)      # -4
ceiling(x)    # -3
floor(x)      # -4

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📏 Trigonometric Functions

Useful in signal processing and scientific applications:

Function	Description
sin(x)	Sine (x in radians)
cos(x)	Cosine
tan(x)	Tangent
asin(x)	Arc sine
acos(x)	Arc cosine
atan(x)	Arc tangent

theta <- pi / 4
sin(theta)    # ≈ 0.707
cos(theta)    # ≈ 0.707

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🧪 Constants and Special Values

R includes some predefined numeric constants:

Constant	Value
pi	3.141593…
Inf	Infinity
-Inf	-Infinity
NaN	Not a Number
NA	Missing value

log(0)        # -Inf
1 / 0         # Inf
sqrt(-1)      # NaN

Use:

is.infinite(Inf)   # TRUE
is.nan(NaN)        # TRUE
is.na(NA)          # TRUE

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📌 Summary – Recap & Next Steps

Numbers and math form the core of statistical programming in R. From simple arithmetic to advanced math functions, R provides everything needed for robust numeric computation.

🔍 Key Takeaways:

• Use numeric, integer, and complex types to handle data precisely
• Use operators like +, %%, ^, and %/% for arithmetic operations
• Leverage built-in functions for rounding, logs, exponentials, and trigonometry
• Handle special values like NA, NaN, and Inf appropriately in your code

⚙️ Real-World Relevance:
Mastering numeric operations in R enables tasks like financial modeling, signal processing, machine learning, and statistical simulations—all grounded in efficient numeric computation.

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❓ FAQs – Numbers and Math in R

❓ How do I ensure a value is stored as an integer?
✅ Add L to the number:

x <- 42L
is.integer(x)  # TRUE

❓ What does %% do in R?
✅ It’s the modulo operator. It returns the remainder:

10 %% 3  # Output: 1

❓ How can I perform integer division in R?
✅ Use %/% to return the integer quotient:

10 %/% 3  # Output: 3

❓ How does R handle NaN, NA, and Inf?
✅ R propagates these values through calculations. Use is.nan(), is.na(), and is.infinite() to detect them.

❓ Can I use degrees in trigonometric functions?
✅ No. R uses radians. Convert degrees using:

deg2rad <- function(deg) deg * pi / 180
sin(deg2rad(30))  # ≈ 0.5

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