R Round to Nearest .5 or .1

R round to nearest .5 or .1

Probably,

round(a/b)*b

will do the work.

> a <- seq(.1,1,.13)
> b <- c(.1,.1,.1,.2,.3,.3,.7)
> data.frame(a, b, out = round(a/b)*b)
     a   b out
1 0.10 0.1 0.1
2 0.23 0.1 0.2
3 0.36 0.1 0.4
4 0.49 0.2 0.4
5 0.62 0.3 0.6
6 0.75 0.3 0.6
7 0.88 0.7 0.7

How to round up to the nearest 10 (or 100 or X)?

If you just want to round up to the nearest power of 10, then just define:

roundUp <- function(x) 10^ceiling(log10(x))

This actually also works when x is a vector:

> roundUp(c(0.0023, 3.99, 10, 1003))
[1] 1e-02 1e+01 1e+01 1e+04

..but if you want to round to a "nice" number, you first need to define what a "nice" number is. The following lets us define "nice" as a vector with nice base values from 1 to 10. The default is set to the even numbers plus 5.

roundUpNice <- function(x, nice=c(1,2,4,5,6,8,10)) {
    if(length(x) != 1) stop("'x' must be of length 1")
    10^floor(log10(x)) * nice[[which(x <= 10^floor(log10(x)) * nice)[[1]]]]
}

The above doesn't work when x is a vector - too late in the evening right now :)

> roundUpNice(0.0322)
[1] 0.04
> roundUpNice(3.22)
[1] 4
> roundUpNice(32.2)
[1] 40
> roundUpNice(42.2)
[1] 50
> roundUpNice(422.2)
[1] 500

[[EDIT]]

If the question is how to round to a specified nearest value (like 10 or 100), then James answer seems most appropriate. My version lets you take any value and automatically round it to a reasonably "nice" value. Some other good choices of the "nice" vector above are: 1:10, c(1,5,10), seq(1, 10, 0.1)

If you have a range of values in your plot, for example [3996.225, 40001.893] then the automatic way should take into account both the size of the range and the magnitude of the numbers. And as noted by Hadley, the pretty() function might be what you want.

What explains the 1 decimal place rounding of x.x5 in R?

Too long to read? Scroll below

This was an interesting study for me personally. According to documentation:

Note that for rounding off a 5, the IEC 60559 standard (see also ‘IEEE
754’) is expected to be used, ‘go to the even digit’. Therefore
round(0.5) is 0 and round(-1.5) is -2. However, this is dependent on
OS services and on representation error (since e.g. 0.15 is not
represented exactly, the rounding rule applies to the represented
number and not to the printed number, and so round(0.15, 1) could be
either 0.1 or 0.2).

Rounding to a negative number of digits means rounding to a power of
ten, so for example round(x, digits = -2) rounds to the nearest
hundred.

For signif the recognized values of digits are 1...22, and non-missing
values are rounded to the nearest integer in that range. Complex
numbers are rounded to retain the specified number of digits in the
larger of the components. Each element of the vector is rounded
individually, unlike printing.

Firstly, you asked "If it is "round to even", why is it 3, i.e. odd number." To be clear, the round to even rule applies for rounding off a 5. If you run round(2.5) or round(3.5), then R returns 2 and 4, respectively.

If you go here, https://stat.ethz.ch/pipermail/r-help/2008-June/164927.html, then you see this response:

The logic behind the round to even rule is that we are trying to
represent an underlying continuous value and if x comes from a truly
continuous distribution, then the probability that x==2.5 is 0 and the
2.5 was probably already rounded once from any values between 2.45 and 2.54999999999999..., if we use the round up on 0.5 rule that we learned in grade school, then the double rounding means that values
between 2.45 and 2.50 will all round to 3 (having been rounded first
to 2.5). This will tend to bias estimates upwards. To remove the
bias we need to either go back to before the rounding to 2.5 (which is
often impossible to impractical), or just round up half the time and
round down half the time (or better would be to round proportional to
how likely we are to see values below or above 2.5 rounded to 2.5, but
that will be close to 50/50 for most underlying distributions). The
stochastic approach would be to have the round function randomly
choose which way to round, but deterministic types are not
comforatable with that, so "round to even" was chosen (round to odd
should work about the same) as a consistent rule that rounds up and
down about 50/50.

If you are dealing with data where 2.5 is likely to represent an exact
value (money for example), then you may do better by multiplying all
values by 10 or 100 and working in integers, then converting back only
for the final printing. Note that 2.50000001 rounds to 3, so if you
keep more digits of accuracy until the final printing, then rounding
will go in the expected direction, or you can add 0.000000001 (or
other small number) to your values just before rounding, but that can
bias your estimates upwards.

Short Answer: If you always round 5s upward, then your data biases upward. But if you round by evens, then your rounded-data, at large, becomes balanced.

Let's test this using your data:

round2 = function(x, n) {
  posneg = sign(x)
  z = abs(x)*10^n
  z = z + 0.5
  z = trunc(z)
  z = z/10^n
  z*posneg
}

x <- data.frame(cbind(
  Number = seq(1.05, 2.95, by = .1), 
  Popular.Round = round2(seq(1.05, 2.95, by = .1), 1),
  R.Round = round(seq(1.05, 2.95, by = .1), 1)))

> mean(x$Popular.Round)
[1] 2.05
> mean(x$R.Round)
[1] 2.02

Using a bigger sample:

x <- data.frame(cbind(
  Number = seq(1.05, 6000, by = .1), 
  Popular.Round = round2(seq(1.05, 6000, by = .1), 1),
  R.Round = round(seq(1.05, 6000, by = .1), 1)))

> mean(x$Popular.Round)
[1] 3000.55
> mean(x$R.Round)
[1] 3000.537

How to round up to whole number in R?

We can use ceiling to do the specified rounding

ceiling(x)
#[1]  6  8 13 14

Rounding numbers to nearest 10 in R

From ?round

Rounding to a negative number of digits means rounding to a power
of ten, so for example ‘round(x, digits = -2)’ rounds to the
nearest hundred.

So,

data <- c(152.335, 39.431, 21.894)
round(data, -1)
#[1] 150  40  20

Round number by rounding units in R

round.to <- function(x, b) {
  round(x/b)*b
}

round.to(value, .2)
## [1]  8.2  1.8  6.4  2.0 10.4

This technique also works for b>1:

round.to(value, 2)
## [1]  8  2  6  2 10

Force R to always round up to two decimal places

If your numbers are in a numeric vector :

format(round(a,digits=2),nsmall=2)

which gives a character vector. The format function is there so that 1 is displayed as 1.00 and not 1 for example. If you don't care about that, omit it.

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If you want 2.3421 to be rounded to 2.35 (not standard rounding but ceiling at 2 decimals), use

format(ceiling(a*100)/100,nsmall=2)

or more legible with pipes:

a %>% multiply_by(100) %>% ceiling %>% divide_by(100) %>% format(2)

Without format: ceiling(a*100)/100 which gives you a numeric.

round numbers to non-decimal numbers

Divide the number by 10, round using either floor or ceil and then multiply by 10.

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