Numbers and Arithmetic

R works like a powerful calculator.

Example

7 + 2
7 - 2
7 * 2
7 / 2
7 %/% 2
7 %% 2
2 ^ 10
10 / 3

Expected output

[1] 9
[1] 5
[1] 14
[1] 3.5
[1] 3
[1] 1
[1] 1024
[1] 3.333333

• / always gives the exact result, including decimals.
• %/% is integer division (drops the remainder); %% gives the remainder — handy for checking whether a number is even.
• ^ raises to a power.
• R prints numbers to 7 significant digits by default, so 10 / 3 shows 3.333333 — but the full precision is kept internally.

Useful math functions

round(3.14159, 2)
signif(123456, 2)
ceiling(3.2)
floor(3.8)
abs(-5)
sqrt(16)
exp(1)
log(100, base = 10)

[1] 3.14
[1] 120000
[1] 4
[1] 3
[1] 5
[1] 4
[1] 2.718282
[1] 2

Special values

1 / 0
-1 / 0
0 / 0
sqrt(2)^2 == 2
isTRUE(all.equal(sqrt(2)^2, 2))

[1] Inf
[1] -Inf
[1] NaN
[1] FALSE
[1] TRUE

• Inf is infinity; NaN means "not a number".
• Decimal numbers are approximate on every computer, so sqrt(2)^2 isn't exactly 2. Compare decimals with all.equal(), which allows for tiny rounding differences.

Common mistakes

• Comparing decimals with ==. Use all.equal() (wrapped in isTRUE() inside if).
• Forgetting that printed values are rounded for display.

Practice

A pizza has 8 slices shared by 3 people. Print how many whole slices each person gets, how many are left over, and the exact share rounded to two decimals.

slices <- 8
people <- 3
slices %/% people
slices %% people
round(slices / people, 2)

[1] 2
[1] 2
[1] 2.67