is 4.58 greater than 4.580

Question

I need to know if 4.58 greater than 4.580

Answer 1

This is a matter of precision using significant digits.  If a recorded measurement is given to you, and an uncertainty is not specified, you may assume there is an uncertainty of ±1 in the last digit.  For example, if 4.58 is such a measurement, then its correct value is known to lie between 4.57 and 4.59, which means you know the value of the measurement to no better than 1 part in 458.  But if the measurement is given as 4.580, then you know the correct value lies between 4.579 and 4.581, so you know the measurement to no better than 1 part in 4580.  This is a much narrower range than knowing it to 1 part in 458.  It represents a more precise measurement of the quantity.  Arithmetically, 4.58 = 4.580, as Somayeh V. pointed out, but in terms of precision of measurement, 4.580 is much more precise then 4.58.  

 

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Answer 2

As real numbers they are equal, but for example if someone is talking about a measurement rounded to two decimal places, 4.58 might have actually been 4.582 or something.