From rounded to the nearest odd digit

Question

I want to round some numbers to the nearest tenth using only odd tenths. eg.

91.15 -> 91.1
91.21 -> 91.3

What is a simple and general equation for this?

Answer 1

This is not rounding to the nearest tenth, but rounding to the nearest fifth (two tenths) with one tenth of an offset. With this in mind, the general equation is:

# Any language where 'round' rounds to the nearest integer
radioStation = round( (original-offset)/interval ) * interval + offset

In Lua:

-- number:   the original value to round
-- interval: the distance between desired values
-- offset:   an optional shifting of the values
function roundToNearest( number, interval, offset )
  offset   = offset   or 0  -- default value
  interval = interval or 1  -- default value
  return math.floor( (number-offset)/interval + 0.5 ) * interval + offset
end

for n=1, 2, 0.09 do
  local result = roundToNearest(n, 0.2, 0.1)
  print(string.format("%.2f : %g", n, result))
end
--> 1.00 : 1.1
--> 1.09 : 1.1
--> 1.18 : 1.1
--> 1.27 : 1.3
--> 1.36 : 1.3
--> 1.45 : 1.5
--> 1.54 : 1.5
--> 1.63 : 1.7
--> 1.72 : 1.7
--> 1.81 : 1.9
--> 1.90 : 1.9
--> 1.99 : 1.9

Answer 2

What about

function roundToOdd(number)
    temp = round(number * 10)
    if number % 2 == 0 then
        if number > temp then
            temp = temp + 1
        else
            temp = temp - 1
        end
    end
    return temp/10
end

Results:

1.10 -> 11.0 -> 11 -> 1.1
1.11 -> 11.1 -> 11 -> 1.1
1.19 -> 11.9 -> 12 -> even -> 11 -> 1.1
1.20 -> 12.0 -> 12 -> even -> 11 -> 1.1
1.21 -> 12.1 -> 12 -> even -> 13 -> 1.3
1.29 -> 12.9 -> 13 -> 1.3
1.36 -> 13.6 -> 14 -> even -> 13 -> 1.3
1.40 -> 14.0 -> 14 -> even -> 13 -> 1.3
1.41 -> 14.1 -> 14 -> even -> 15 -> 1.5