Significant figures are the digits in a number that carry meaning in regards to the precision of the measurement. They are used to indicate the level of uncertainty or the degree of accuracy of a measurement. A number which is not a measured value has an infinite number of significant figures. In this response, we will discuss why this is the case.





Significant figures are the digits in a number that are known with certainty plus one uncertain digit. For example, if a length is measured with a ruler marked off in millimeters, we can be certain of the whole millimeters and one uncertain digit. Therefore, the number of significant figures in the measurement is two.



Measured values have finite significant figures because the accuracy of a measurement is limited by the precision of the measuring instrument. For example, a ruler marked off in millimeters can only measure lengths to the nearest millimeter. Therefore, the accuracy of a length measured with this ruler is limited to the nearest millimeter.



Non-measured values, such as mathematical constants and exact values, have infinite significant figures because they are defined precisely and are not subject to measurement error. For example, the value of pi, which is the ratio of the circumference of a circle to its diameter, is an exact value that is defined precisely. Its value is approximately 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679..., and it has an infinite number of significant figures.



In conclusion, a number which is not a measured value has an infinite number of significant figures because it is defined precisely and is not subject to measurement error. Measured values, on the other hand, have finite significant figures because their accuracy is limited by the precision of the measuring instrument.

Exact number are not measured . They have no uncertainity and an infinite numbers of significant figures. Measured numbers: Mass is an example of a measured number. When mass is reported as 0•5237g, as shown on the scale, it is more precise than a mass reported as 0•5g..