How can I measure a resistance very accurately more than a multimeter (ohmmeter)?
For our measurement we are using resistances with values such as 300.8974083. But the instrumentation is very old from many years ago. I am asked to measure the resistance again but the multimeter is measuring very roughly (not accurately with enough digits). Is there a method to measure a resistance accurately?
You can't.
Very few people, if any, regardless of how much was spent on equipment, will be able to measure resistance to 10 significant digits. If such equipment does actually exist somewhere, then those allowed to be in the same room with it don't have to ask here how to make such a measurement. Anyone that does ask here isn't going to be allowed in that lab, hence there is no way for you to make this measurement.
Stop and actually think about what you are asking for. You are looking for about 1 part in 330 x 1012. That's so tiny that even parts per million (PPM) is not a useful measure. Your accuracy requirement is 1/3 of part per billion (1/3 x 109).
Consider that if your resistor changes by only .1 PPM / °C (even "good" resistors are in the 10s of PPM/°C) that you still have to hold the temperature at a known constant level to within 1/300 of a °C. That alone would require substantial sophisticated equipment. Then there will be many other sources of error that we can happily ignore at .1% but that become overwhelming sources of error at .3 PPB. To put this in perspective, that's measuring the circumference of the earth to within a 1/2 inch.
It's simply not going to happen. Forget about it.
A straightforward way of improving the accuracy of a resistance measurement is to use a "4-wire" measurement.
Resistance measurements are done by applying a stimulus current, and measuring the voltage across the resistor. The 4-wire measurement uses separate leads for the stimulus and measurment:
simulate this circuit – Schematic created using CircuitLab
This prevents the parasitic lead resistances (Rpar1 and Rpar2 in the schematic) from being measured as part of the resistor you're trying to measure.
As an example, the Agilent 34401A benchtop multimeter can measure a 1 kOhm resistor with 0.0025% accuracy in 4-wire mode (+/- .025 Ohms), but only with +/- 0.2 Ohms in 2-wire mode.
At 300 Ohms a .025 Ohm error is .008% which seems to be within your actual requirements, even if it doesn't give the number of digits of precision you first stated.
Of course the Wheatstone bridge that you and other answers have mentioned is another option that might be more affordable if you are measuring a limited range of resistor values, or if you are only interested in binning resistors for equal values rather than knowing the actual exact values.
How can I measure a resistance very accurately more than a multimeter(onmmeter)?
We need to be careful not to confuse precision with accuracy.
1. Buy a better meter.
A typical inexpensive hand-held multimeter has 3½ digits (accuracy 0.5% ∓2 digits).
A better hand-held multimeter may have 4½ digits (accuracy 0.1% ∓1 digits).
A good bench multimeter may have 8½ digits (accuracy 2.2 ppm).
I ... can buy some resistances
2. Use a better measurement technique
See Wheatstone bridge.
Here is how they do it at the National Institute of Standards.. The lowest uncertainty for resistance is the Quantum Hall standard.
