CCNA1 v3 Module 2 W04 – Sault College – Bazlurslide 1 Accuracy vs. Precision

PHY115 – Sault College – Bazlurslide 2 Physics It comes from the Latin word “physica”, meaning nature. Physics is the study of laws of nature that govern the physical world around us. Physics is the branch of science that deals with the properties, changes, and interactions of matter and energy.

PHY115 – Sault College – Bazlurslide 3 Physics Physics is an important science: it increases our understanding of numerous phenomena; It is the foundation for further studies in science, engineering, and technology; and it is the stepping stone to many careers.

PHY115 – Sault College – Bazlurslide 4 Measurement Measurement is a process of comparing an unknown value to a known value. A measurement may be expressed in terms of its accuracy or its precision.

PHY115 – Sault College – Bazlurslide 5 Accuracy vs. Precision Accuracy: A measure of how close an experimental result is to the true value. Precision: A measure of how exactly the result is determined. It is also a measure of how reproducible the result is. –Absolute precision: indicates the uncertainty in the same units as the observation –Relative precision: indicates the uncertainty in terms of a fraction of the value of the result

PHY115 – Sault College – Bazlurslide 6 Accuracy Physicists are interested in how closely a measurement agrees with the true value. This is an indication of the quality of the measuring instrument. Accuracy is a means of describing how closely a measurement agrees with the actual size of a quantity being measured.

PHY115 – Sault College – Bazlurslide 7 Error The difference between an observed value and the true value is called the error. The size of the error is an indication of the accuracy. Thus, the smaller the error, the greater the accuracy. The percentage error determined by subtracting the true value from the measured value, dividing this by the true value, and multiplying by 100.

PHY115 – Sault College – Bazlurslide 8 Error

PHY115 – Sault College – Bazlurslide 9 Significant Digits The accuracy of a measurement is indicated by the number of significant digits. Significant digits are those digits in the numerical value of which we are reasonably sure. More significant digits in a measurement the accurate it is:

PHY115 – Sault College – Bazlurslide 10 Significant Digits More significant digits in a measurement the accurate it is: E.g., the true value of a bar is 2.50 m Measured value is 2.6 m with 3 significant digits. The percentage error is ( )*100/2.50 = 4% E.g., the true value of a bar is 2.50 m Measured value is 2.55 m with 3 significant digits. The percentage error is ( )*100/2.50 = 0.2% Which one is more accurate? The one which has more significant digits

PHY115 – Sault College – Bazlurslide 11 Precision Being precise means being sharply defined. The precision of a measuring instrument depends on its degree of fineness and the size of the unit being used. Using an instrument with a more finely divided scale allows us to take a more precise measurement.

PHY115 – Sault College – Bazlurslide 12 Precision The precision of a measuring refers to the smallest unit with which a measurement is made, that is, the position of the last significant digit. In most cases it is the number of decimal places. E.g., The precision of the measurement 385,000 km is 1000 km. (the position of the last significant digit is in the thousands place.) The precision of the measurement 0.025m is 0.001m. (the position of the last significant digit is in the thousandths place.)

PHY115 – Sault College – Bazlurslide 13 How precise do we need? Physicists are interested in how closely a measurement agrees with the true value. That is, to achieve a smaller error or more accuracy. For bigger quantities, we do not need to be precise to be accurate.

PHY115 – Sault College – Bazlurslide 14 How precise do we need? For bigger quantities, we do not need to be precise to be accurate. E.g., the true value of a bar is 25 m Measured value is 26 m with 2 significant digits. The percentage error is (26-25)*100/25 = 4% E.g., the true value of a bar is 2.5 m Measured value is 2.6 m with 2 significant digits. The percentage error is ( )*100/2.5 = 4% Which one is more precise? The one which has the precision of 0.1m Which one is more accurate? Both are same accurate as both have 2 significant digits

PHY115 – Sault College – Bazlurslide 15 Accuracy or Relative Precision An accurate measurement is also known as a relatively precise measurement. Accuracy or Relative Precision refers to the number of significant digits in a measurement. A measurement with higher number of significant digits closely agrees with the true value.

PHY115 – Sault College – Bazlurslide 16 Estimate Any measurement that falls between the smallest divisions on the measuring instrument is an estimate. We should always try to read any instrument by estimating tenths of the smallest division.

PHY115 – Sault College – Bazlurslide 17 Accuracy or Relative Precision In any measurement, the number of significant figures are critical. The number of significant figures is the number of digits believed to be correct by the person doing the measuring. It includes one estimated digit. A rule of thumb: read a measurement to 1/10 or 0.1 of the smallest division. This means that the error in reading (called the reading error) is 1/10 or 0.1 of the smallest division on the ruler or other instrument. If you are less sure of yourself, you can read to 1/5 or 0.2 of the smallest division.

PHY115 – Sault College – Bazlurslide 18 Exact vs. Approximate numbers An exact number is a number that has been determined as a result of counting or by some definition. 41 students are enrolled in this class 1 in = 2.54 cm Nearly all data of a technical nature involve approximate numbers. That is numbers determined as a result of some measurement process, as with a ruler. No measurement can be found exactly.

PHY115 – Sault College – Bazlurslide 19 Calculations with Measurements The sum or difference of measurements can be no more precise than the least precise measurement. Round the results to the same precision as the least precise measurement mm Using a micrometer 54 mm Using a ruler, Precision of the ruler is 1 mm But actually it can be anywhere between to mm This means that the tenths and hundredths digits in the sum mm are really meaningless, the sum should be 96 mm with a precision of 1 mm

PHY115 – Sault College – Bazlurslide 20 Calculations with Measurements The product or quotient of measurements can be no more accurate than the least accurate measurement. Round the results to the same number of significant digits as the measurement with the least number of significant digits. ouse/labs/Scimeth/mr-sigfg.htmlhttp:// ouse/labs/Scimeth/mr-sigfg.html Length of a rectangle is 54.7 m Width of a rectangle is 21.5 m Area is m 2 Area should be rounded to 1180 m 2 To express with same accuracy

PHY115 – Sault College – Bazlurslide 21 Examples of Rounding ouse/labs/Scimeth/mr-sigfg.htmlhttp:// ouse/labs/Scimeth/mr-sigfg.html