This new first part is in response to a query.
color(blue)("Additional explanation: demonstration of rounding by example")Additional explanation: demonstration of rounding by example
I chose to use the number 23.42123.421 as the starting point for my example
Round to 2 decimal places
23.42color(red)(1) ->23.421→round down as color(red)( 1) <5 ->23.421<5→23.42
23.42color(red)(2) ->23.422→round down as color(red)( 2) <5 ->23.422<5→23.42
23.42color(red)(3) ->23.423→round down as color(red)( 3) <5 ->23.423<5→23.42
23.42color(red)(4) ->23.424→round down as color(red)( 4) <5 ->23.424<5→23.42
23.42color(red)(5) ->23.425→round up as color(red)( 5) >=5 ->23.435≥5→23.43
23.42color(red)(6) ->23.426→round up as color(red)( 6) >=5 ->23.436≥5→23.43
23.42color(red)(7) ->23.427→round up as color(red)( 7) >=5 ->23.437≥5→23.43
23.42color(red)(8) ->23.428→round up as color(red)( 8) >=5 ->23.438≥5→23.43
23.42color(red)(9) ->23.429→round up as color(red)( 9) >=5 ->23.439≥5→23.43
23.43color(red)(0) ->23.430→round down as color(red)( 0) <5 ->23.430<5→23.43
23.43color(red)(1) ->23.431→round down as color(red)( 1) <5 ->23.431<5→23.43
23.43color(red)(2) ->23.432→round down as color(red)( 2) <5 ->23.432<5→23.43
23.43color(red)(3) ->23.433→round down as color(red)( 3) <5 ->23.433<5→23.43
23.43color(red)(4) ->23.434→round down as color(red)( 4) <5 ->23.434<5→23.43
23.43color(red)(5) ->23.435→round up as color(red)( 5) >=5 ->23.445≥5→23.44
23.43color(red)(6) ->23.436→round up as color(red)( 6) >=5 ->23.446≥5→23.44
And so on:
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color(blue)("Answering the question")Answering the question
By calculator 2sqrt(3) = 3.46410....
The dots indicate that the digits go on for a very long time.
As we need the last digit to be the 10^("ths"), the cut off point is:
color(green)(3.4color(red)(|)6410....)
color(white)(3.4)color(red)(uarr)
color(red)("Cut off point")
We now consider the 3 units+4/10+6/100
The digit to the right is 6. As this satisfies the condition of 5 or more we round up the 4 by 1 and consider all the digits to the right of the cut off point as 0's:
color(green)(3.5000..) = 3.5
