Chapter 2, Problem 2.37EP

Interpretation Introduction

Interpretation:

Given table has to be completed using the number of significant figures, estimated digit and magnitude of uncertainty for the given number in the first column.

Concept Introduction:

Whenever a measurement is made, the significant figures in the measured quantity give the actual measurement.  For this the significant figures should be recognized first. The significant figures may be non-zero digit and zero digit.  But Zero may be or may not be a significant figure.  It depends on where the zero appears.  Leading zeros in the front of any number are never significant.  Zeros between the numbers are significant.  When an object is measured with a scale having graduations in centimeter, and if the length of the object falls between 5 and 6, the estimated length would be 5.2 cm.  But this value is approximate.  This is called the uncertainty error.  If the same scale is graduated in tenths of a centimeter, the measurement made would be with less degree of uncertainty.  Hence if the markings become smaller, lesser is the degree of uncertainty.  Also when any measurement is made, the last number that indicates the actual measurement is termed as estimated digit due to its less uncertainty.  The magnitude of measurement and uncertainty of measurement are the two most important information to be conveyed in order to show case the values more exact.  The significant figures any measurements are said to convey the uncertainty, while the digit values convey the magnitude.