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Why do we face a problem of not getting to the exact answer but to an approx to it, mostly everything we come through in practical physics is a approx but not the exact one.

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  • $\begingroup$ There are uncertainties in every measurement, and the mathematical model that you are using is only an approximation of the physics experiment that you are doing. For example, if you are using pulleys in your experiment, you will not have an easy time of knowing how much friction force exists in the pulleys, how much the weight of the string affects the answer, how much any air currents in the room affect the answer, etc. $\endgroup$ – David White Aug 17 at 22:06
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Try to measure the width of a strawberry with a ruler. You might measure $1.7 \mathrm{cm}$, or $1.75 \mathrm{cm}$ if you have a good eye. But no deeper. You simply can't see what the third decimal would be - and the millimetre scale on the ruler is of no help below the millimetre range.

You don't know if the third decimal is a $1$ or a $7$ or so. The number $1.75 \mathrm{cm}$ is not necessarily accurate, because accurate would mean $1.75000000... \mathrm{cm}$. Surely, you don't know that this is the case. So, your measurement is not 100 % accurate.

  • The ruler is split into millimetres. Its accuracy is limited to the millimetre range.
  • Your keen eye may be able to see if the measurement is halfway in-between or maybe a third in-between two millimetre ticks. That might increase the accuracy of this measurement slightly to within half a millimetre or so.
  • Use a micrometre screw gauge, and you have one deeper magnitude of accuracy. One extra decimal. It is now the fourth or fifth decimal that you are unsure about.
  • Use an optical microscope and you can magnify some hundreds of times and read of a much more accurate reading. But it is limited around the micrometre range.
  • Use an electron microscope to zoom in a million times. But more accurate. But it reaches its limit in the nanometre range.

Any real-life measurement tool and device has a limit of accuracy. Beyond that limit, we simply can't know the following decimals. So, we simply can't call it 100 % accuracy. Since there might be infinitely many decimals, and any device we ever invent will always have a finite accuracy limit, no device will ever reach 100 % accuracy.

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It is because we use some sort of reduced requirements to our data (phenomena). The exact information may give you one exact point, but it requires an infinite amount of specifications. Take for example apples. We count them despite they are different.

As soon as you increase the number of your requirements, the countability may be lost. So we content ourselves with a reduced criteria to the data in order to make them quantitative.

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