Paying attention to the number of significant figures lets you avoid irrelevant precision and unnecessary computation and helps you perform necessary computation. It helps you estimate values and errors.
For example, the value of Pi is known to more than 1.2 million million decimal places, but we often use 22/7 in school calculations. 22/7 agrees with the actual number only to 3 significant digits. When we need more accuracy, the ratio 355/113 can be used. It agrees with the actual value for 7 digits.
Understanding significant digits lets us avoid the trap of assuming high precision means high accuracy. The population of a city may be stated as 3,054,276, but there may never have been a point in time when the actual number of people within the city limits was equal to that value. More likely, that value is within about 10,000 of the population on some given day. In other words, the accuracy is probably no better than 3 significant digits.
For example, the value of Pi is known to more than 1.2 million million decimal places, but we often use 22/7 in school calculations. 22/7 agrees with the actual number only to 3 significant digits. When we need more accuracy, the ratio 355/113 can be used. It agrees with the actual value for 7 digits.
Understanding significant digits lets us avoid the trap of assuming high precision means high accuracy. The population of a city may be stated as 3,054,276, but there may never have been a point in time when the actual number of people within the city limits was equal to that value. More likely, that value is within about 10,000 of the population on some given day. In other words, the accuracy is probably no better than 3 significant digits.