 Hello and welcome to this session. In this session we will choose the level of accuracy at which you use two limitations on measurement when we purchase quantities. First of all, let us discuss accuracy. Now accuracy is how much is the measured value to the actual measure or true value. For example, if you throw four dots and all the four hit the bull's eye, then this is called accuracy. Now let us discuss precision. It is a measure of measurement to be consistently reproduced and precise measurements are close to each other. For example, if you throw four dots and all the four hit the same spot, then this is called precision. Now let us see one example to find accuracy and precision. Now suppose actual temperature is 38 degrees Fahrenheit outside the room. Now when we measured the temperature in degrees Fahrenheit 10 times, we found the following readings and the readings are 38.0, 38.0, 37.8, 38.1, 38.0, 37.9, 38.0, 38.2, 38.0 and 37.9. Now all these readings are in degrees Fahrenheit. Now see, all the readings show a tendency toward a particular value. So there is consistency in the readings and hence there is high precision and also all the values are very near to the actual temperature each time. So there is high accuracy. So here we have high precision and high accuracy. Now we shall see how to determine which measurement is more precise. Now you ask two friends for the time. My view says it's about 315 p.m. and Geo says it is 313 and 22 seconds. Then we say that Geo gives more precise measurement of the time because Geo gives the time to the nearest second. Thus we see that precision is the level of detail that an instrument can measure. In a similar way a ruler marked in millimeters is more precise than the ruler marked in centimeters because millimeter smaller unit than centimeter monitors discuss value of significant digits in precision. Now the precision of the measurement depends on the unit of measure being used. The digits you record when the measure are called significant digits and these digits indicate the precision of the measurement like 3.1415 is more precise than 3.14 because 3.14 has only 3 significant digits and 3.1315 has 5 significant digits. Now let us discuss the latest possible error. Now see the following diagram. A block of wood is placed along the edge of a ruler that is marked in touch of an edge. Now friend we might say that block of wood is 3.7 inches long. Let's put our measurement exact. This measurement is approximate. Now when we say length of block of wood is 3.7 inches we mean it is 2.7 inches long which is 2.6 inches or 2.8 inches therefore 3 measure of block of wood is between 2.65 inches and 2.75 inches. In other words the 3 measure is less than 0.05 inches from 2.7 and is greater than 0.05 inches from 3.7 and when we written as 2.7 plus minus 0.05 inches the value 0.05 is called greatest possible error of measurement and is half of the place value of last digit and we can say that the greatest possible error is one half the place value of the last significant digit. As you can see in 2.7 last significant digit is 7 which is at tenth space so greatest possible error is half of 1 by 10 that is 0.05. Now in measurement of 4,500 feet last significant digit is 5 which is at hundred space so greatest possible error is equal to half of hundred that is equal to 50 and we write the measurement as 1,500 plus minus 50 feet normal. Out of 3 numbers having 3 units of measurement remember having least error is not precise for example in 3 centimeters and 3.7 centimeters error in 3 is 0.5 and error in 3.7 is 0.05. Now the least error is in 3.7 centimeters that is 0.05 so it is not precise measurement. Now out of 3 numbers having same units of measurement number having more significant digits is not accurate. Precision also depends on the units of measurement if the units of measurement are different in 2 different numbers like 3 centimeters and 3.8 centimeters then smaller unit is more precise unit of measurement so here 3 centimeters is more precise unit of measurement as centimeters is smaller unit. Now let us see how to calculate values which give more accurate results. When we add or multiply 2 given numbers then the obtained answer should have as many significant digits as in the number having least significant digits from the given numbers it means answer should be no more precise than the least precise measurement. Now let us discuss an example. Now let us find area of rectangle whose dimensions are 12.3 centimeters by 16.86 centimeters. Now see area of rectangle will be equal to length into width so this is equal to 12.3 centimeters into 16.86 centimeters which is equal to 207.378 centimeters square. Now here we can see in the answer we have 6 significant digits but least number of significant digits are in 12.3 that is 3 it means 12.3 is least precise number our answer should also contain 3 significant digits it should be no more precise than the least precise measurement. So that is the given answer to 3 significant digits so we have area is equal to 207 centimeters square. Now here we have rounded it off to 3 significant digits so in this session we have discussed about accuracy and precision of measurement and this completes our session. Hope you all have enjoyed this session.