Physicists Biographies

# Understanding significant figures

It is very common for engineers, foremen, bricklayers, seamstresses to use a measuring instrument, such as a meter, a tape measure, etc. What we can say about these examples is that each one of them, when using the meter, is performing a comparison between quantities. Even when, for example, we solve calculation exercises, we are comparing quantities.

When we measure a quantity we always find a value, then we say that such a value has a precision limited by factors such as experimental uncertainty, which is related to any type of object or instrument used, or even to the skill of the person performing the experiment, that is, , the experimenter; and is also associated with the number of times the experiment is tested.

Let’s see the figure above, in it we have a common school ruler, whose smallest division is given in millimeters and the largest, in centimeters, that is, 1 in 1 cm.

If we express any measurement by 8.6 cm, the decimal value of this measurement must be better evaluated if the ruler presents divisions smaller than 1 cm. If, through the figure above, we measure our thumb, we can say that its length is greater than 3 cm. If our ruler presents values ​​smaller than 1 cm, we have the possibility to measure the size of the thumb accurately, now if we use a ruler that presents measurements only in centimeters, we can say that it will be impossible to determine the exact size of the thumb.

So when we say that the finger (thumb) size is 3.5 cm, we are actually stating a result with two significant figures, so 3 and 5 are our significant figures, with 3 being the correct figure and 5 being the correct figure. doubtful.

Rounding off values

When performing mathematical operations with significant figures, it is necessary, in many cases, to consider an approximation of the measure with a smaller number of significant figures. Rounding is the name we give to this process. To correctly perform a rounding, we must follow the following rules:

to . If the digit to be eliminated is greater than or equal to five, we add a unit to the first digit on the left.

2nd If the digit to be eliminated is less than five, we must keep the left digit unchanged.

Thus, for example, if we have to leave the values ​​with only 2 significant figures, we will have: 9.74 ≈ 9.7 and 9.88 ≈ 9.9, according to the criterion used for rounding.