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1. Any number that isn't a zero is always a sig fig.
2. Zeroes that are between two non-zeroes are always sig figs.
3. Zeroes that don't have any non-zeroes before them are not sig figs (this includes leading zeroes).
4. Zeroes that come at the end of a number are sig figs only if the number contains a decimal point.

console.assert(sigFigs('-0') === 1, '-0' + ' fails with ' + sigFigs('-0'));
console.assert(sigFigs('0.0') === 1, '0.0' + ' fails with ' + sigFigs('0.0'));
console.assert(sigFigs('-0.00') === 2, '-0.00' + ' fails with ' + sigFigs('-0.00'));
console.assert(sigFigs('0e5') === 1, '0e5' + ' fails with ' + sigFigs('0e5'));
console.assert(sigFigs('-0.0e5') === 1, '-0.0e5' + ' fails with ' + sigFigs('-0.0e5'));
console.assert(sigFigs('-0.0e-5') === 1, '-0.0e-5' + ' fails with ' + sigFigs('-0.0e-5'));
console.assert(sigFigs('1000') === 1, '-1000' + ' fails with ' + sigFigs('1000'));
console.assert(sigFigs('-1000.') === 4, '1000.' + ' fails with ' + sigFigs('-1000.'));
console.assert(sigFigs('.1000') === 4, '-.1000' + ' fails with ' + sigFigs('.1000'));
console.assert(sigFigs('-0.1000') === 4, '.1000' + ' fails with ' + sigFigs('-0.1000'));
console.assert(sigFigs('1010') === 3, '-1010' + ' fails with ' + sigFigs('1010'));
console.assert(sigFigs('-1e3') === 1, '-1e3' + ' fails with ' + sigFigs('-1e3'));
console.assert(sigFigs('1.00e3') === 3, '1.00e3' + ' fails with ' + sigFigs('1.00e3'));
console.assert(sigFigs('-1200.0034') === 8, '-1200.0034' + ' fails with ' + sigFigs('-1200.0034'));
console.assert(sigFigs('1200.0034e8') === 8, '1200.0034e8' + ' fails with ' + sigFigs('1200.0034e8'));
console.assert(sigFigs('1200.0034e-8') === 8, '1200.0034e-8' + ' fails with ' + sigFigs('1200.0034e-8'));
console.assert(sigFigs('-1234') === 4, '-1234' + ' fails with ' + sigFigs('-1234'));
console.assert(sigFigs('1234.1234') === 8, '1234.1234' + ' fails with ' + sigFigs('1234.1234'));
console.assert(sigFigs('-00001000') === 1, '-00001000' + ' fails with ' + sigFigs('-00001000'));
console.assert(sigFigs('00001000.0000') === 8, '00001000.0000' + ' fails with ' + sigFigs('00001000.0000'));
console.assert(sigFigs('-00001000.00001') === 9, '-00001000.00001' + ' fails with ' + sigFigs('-00001000.00001'));
console.assert(sigFigs('-0.1234') === 4, '.1234' + ' fails with ' + sigFigs('.1234'));
console.assert(sigFigs('-.12340000') === 8, '-.12340000' + ' fails with ' + sigFigs('.12340000'));
console.assert(sigFigs('-.00001234') === 4, '-.00001234' + ' fails with ' + sigFigs('-.00001234'));
console.assert(sigFigs('-123400001234') === 12, '123400001234' + ' fails with ' + sigFigs('123400001234'));
console.assert(sigFigs('-12340001234.1234') === 15, '-12340001234.1234' + ' fails with ' + sigFigs('-12340001234.1234'));

console.assert(parseFloat(multiply('20', '1234')) === 20000 && sigFigs(multiply('20', '1234')) === 1, '20 * 1234' + ' fails with ' + multiply('20', '1234'));

/* Copyright (C) 2013 Sushain Cherivirala
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see [http://www.gnu.org/licenses/].
 */

function sigFigs(x) {
	var sf;
	x = x.toString(); //force x to be a String
	x = x.replace(/^[\-\+]+/, '') //remove + or - sign

	if(isNaN(x)) {
		alert('Invalid input: ' + x);
		throw new Error('Invalid input');
	}
	else if(parseFloat(x) === 0) { //handle corner case of 0
		if(x.search(/^0+(e[0-9]+)?$/) === 0) //if no more precise than 0
			sf = 1;
		else {
			x = x.replace(/^0+/, '') //remove all leading zeroes
			x = x.replace(/\./, '').replace(/e[\-\+]*[0-9]+/, ''); //remove decimal point and exponential notation
			sf = x.length;
		}
	}
	else {
		x = x.replace(/^0+/, '') //remove all leading zeroes

		var sf = 0;
		var ePoint = x.toLowerCase().indexOf('e'); //find exponential form marker
		if(ePoint !== -1) {
			x = x.replace(/\./, '').replace(/e[\-\+]*[0-9]+/, ''); //remove decimal point and exponential notation
			sf = x.length;
		}
		else
		{
			var iPart, fPart; //extract integral part and mantissa
			var dPoint = x.indexOf('.');
			if(dPoint !== -1) {
				if(dPoint === (x.length - 1)) { //handle decimal point at end of number
					sf = dPoint;
				}
				if(dPoint === 0) { //handle decimal point at start of number
					x = x.replace(/\./, '').replace(/^0+/, ''); //remove decimal point and all leading zeroes
					sf = x.length;
				}
				else { //handle decimal point in middle of number
					sf = x.length - 1;
				}
			}
			else {
				x = x.replace(/0*$/, ''); //remove trailing zeroes
				sf = x.length;
			}
		}
	}
	return sf;
}

function multiply(x, y) {
	var xNum = parseFloat(x), yNum = parseFloat(y);
	return (xNum * yNum).toPrecision(Math.min(sigFigs(x), sigFigs(y)));
}

function divide(x, y) {
	var xNum = parseFloat(x), yNum = parseFloat(y);
	return (xNum / yNum).toPrecision(Math.min(sigFigs(x), sigFigs(y)));
}