javascript - Why are some scientific numbers automatically rounded and others aren't? -

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why numbers in scientific notation starting 9.999999999999999 rounded 1 while others remain same?

for example, in google chrome 20 following happens.

(9.999999999999999e+306).tostring() === "9.999999999999999e+306" // true

but

(9.999999999999999e+303).tostring() === "1e+304" // true

why that? floating point issue?

however strangest thing in opera 11.64 (1e23).tostring() === "9.999999999999999e+22". tried report 1e23 bug opera no 1 replied.

live demo here: http://jsfiddle.net/3ekdk/3/

source code of demo

var console = console || {}; console.logtobody = function( str ){     document.body.innerhtml += "" + str + "<br/>"; };       var parts = ["9.999999999999999e", 310 ], tmp, tmp2; while( parts[1]-- ){     tmp = +(parts.join(''));     if( /9.9{3,}e/.test( +tmp ) ){         console.logtobody( tmp + " doesn't convert " +  (+tmp).toprecision(1) );     }     tmp2 = "1e"+parts[1];     //carakan javascript engine math bug:     if( !/^1e*/.test( +tmp2 ) ){         console.logtobody( tmp2 + " = " + (+tmp2) + " in runtime environment.");     } }

it's because floating point numbers approximation. numbers can't represented floating point format, is, binary fraction, approximated http://en.wikipedia.org/wiki/ieee_754-2008

that why should never rely on floating point arithmetic without rounding it. simple example following:

> 20.61 - .1   20.509999999999998

here's great explanation of floating point format http://www.randelshofer.ch/fhw/gri/float.html#chapterfloatingpointformat

ordinary decimal 178.125

scientific decimal 1.78125 e 102

scientific binary 1.0110010001 e 2111


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