Javascript conditional find/replace

One approach, is the following (using plain JavaScript, albeit you'll need to use an up-to-date browser):

// first, we need to get all the 'li' items:

var lis = document.querySelectorAll('ul > li'),
    // find the relevant text-property for this browser:
    textProp = 'textContent' in document ? 'textContent' : 'innerText',
    // empty string variable to allow assessment of changes:
    _newText = '';

// Remap the bullet list entries to a new (consistent) tag type (your choice – make it look pretty!).
// do this one yourself.

// a function to zero-pad the numbers (I believe a requirement of Dewey Decimal):
function leftPadNumber(num, numLength, padChar) {
    var nString = num.toString(),
        major = parseInt(num, 10),
        minor = parseFloat(nString.substring(nString.indexOf('.'))),
        diff = numLength - major.toString().length;
    if (diff > 0) {
        return new Array(diff + 1).join(padChar || 0) + (major + minor);
    } else {
        return num;
    }

}

// For entries between 100 and 200, add 100 to the Dewey decimal number.
// For entries between 400 and 500, add 200 to the Dewey decimal number.
// Entries between 850 and 900 need to have 100 removed from the Dewey decimal number.
// Entries between 600 and 650 need to have 17 added to the Dewey decimal number

// note that I've taken a very literal interpretation of 'between' (amend if necessary):
function amendedDeweyDecimal(num) {
    if (num > 100 && num < 200) {
        num += 100;
    } else if (num > 400 && num < 500) {
        num += 200;
    } else if (num > 850 && num < 900) {
        num -= 100;
    } else if (num > 600 && num < 650) {
        num += 17;
    }
    // happens if num falls somewhere outside of the above constraints:
    return num;
}

// iterates over each element in the 'lis' nodeList/collection:
[].forEach.call(lis, function (a) {
    /* replaces the found numbers ('m') in the string, using the two
       functions, above, and assigns those to the _newText variable:
    _newText = a[textProp].replace(/(\d{3}\.\d{2})/, function (m) {
        return leftPadNumber(amendedDeweyDecimal(parseFloat(m)).toFixed(2), 3);
    });

    // For items that get changed, append “changed” to the record.
    // For items that do not get changed, append “no change” to the record.

    // returns the original text to the element, along with '(no change)'
    // (if 'a[textProp]' is exactly equal to '_newText') or with '(changed)'
    // (if the two variables are not identical):
    a[textProp] = _newText + ' (' + (_newText === a[textProp] ? 'no change' : 'changed') + ')';
});

// For records that are incorrect, append “invalid record” to the record
// I have absolutely no idea how to assess an 'incorrect' record.

JS Fiddle demo.

References:

• Array.prototype.forEach().
• document.querySelectorAll().
• Number.toFixed().
• Number.toString().
• String.parseFloat().
• String.parseInt().
• String.replace().

try jQuery .each

$('li').each(function(index, value) {
    var val = $(this).text().split(','); //split into array
    if (index >= 100 && index < 200) {
        //do stuff
    }
    if (index >= 400 && index < 500) {
        //do stuff
    }
    //etc
});

Regardless if you want to solve this using pure JavaScript or a helper library (like jQuery for example), i would suggest to disassemble your problem into smaller tasks and solve them one by one. At the end they will fit one into another and will build the complete solution. I would have started with three simple functions (reading your description they will be needed often):

• the ability to list all LI elements separately
• extract the number from the LI content
• check if the number in in a given range

The code can look like this:

// count of all LI items
var elements = 0; 
// fetch LI item one at a time
var element = document.getElementById(elements+1);
while (element != undefined) {
    // get the number
    var number = Number(getNumber(element.innerHTML));
    // do something with number and or LI element
    if (inRange(number, 100, 200)) { /* add 100 ...*/ } // and so on
    // go to next element
    elements++;
    element = document.getElementById(elements+1);
}

function getNumber(elementContent) {
    return elementContent.split(",")[0]; // TODO error handling
}

function inRange(number, min, max) {
    return (number >= min) && (number <= max);
}

You can introduce simple objects and arrays to store information and states to track the changes of your content.