The accuracy indicates how close the measured value is from its actual value, i. Precision refers to the random spread of the measured values. This is caused by thermal noise in the measuring circuit of the measuring equipment and the measurement set-up.
Accuracy and Precision This is important because bad equipment, poor data processing or human error can lead to inaccurate results that are not very close to the truth. Precision is how close a series of measurements of the same thing are to each other. The accuracy is a measure of the degree of closeness of a measured or calculated value to its actual value. The percent error is the ratio of the error to the actual value multiplied by The precision of a measurement is a measure of the reproducibility of a set of measurements.
Some other numbers are exact; for example, there are exactly 2. Significant Figures and Mathematical Operations. If the first digit to be discarded is a 4 or less, the value of the last digit retained is not changed. Which measuring apparatus would you use to deliver 9. To how many significant figures can you measure that volume of water with the apparatus you selected?
Use the 10 mL graduated cylinder, which will be accurate to two significant figures. Mathematical operations are carried out using all the digits given and then rounding the final result to the correct number of significant figures to obtain a reasonable answer.
This method avoids compounding inaccuracies by successively rounding intermediate calculations. After you complete a calculation, you may have to round the last significant figure up or down depending on the value of the digit that follows it. If the digit is 5 or greater, then the number is rounded up. For example, when rounded to three significant figures, 5. Similarly, to three significant figures, 5. The procedures for dealing with significant figures are different for addition and subtraction versus multiplication and division.
When we add or subtract measured values, the value with the fewest significant figures to the right of the decimal point determines the number of significant figures to the right of the decimal point in the answer.
Drawing a vertical line to the right of the column corresponding to the smallest number of significant figures is a simple method of determining the proper number of significant figures for the answer:. The line indicates that the digits 3 and 6 are not significant in the answer. These digits are not significant because the values for the corresponding places in the other measurement are unknown Consequently, the answer is expressed as Again, numbers greater than or equal to 5 are rounded up.
If our second number in the calculation had been When we multiply or divide measured values, the answer is limited to the smallest number of significant figures in the calculation; thus,. Although the second number in the calculation has four significant figures, we are justified in reporting the answer to only three significant figures because the first number in the calculation has only three significant figures.
An exception to this rule occurs when multiplying a number by an integer, as in In this case, the number of significant figures in the answer is determined by the number The correct answer is therefore When you use a calculator, it is important to remember that the number shown in the calculator display often shows more digits than can be reported as significant in your answer.
Remember, the answer must only have 1 doubtful digit. The answer must be rounded off to 2 significant figures, since 1. The answer must be rounded off to 3 significant figures, since Give the correct number of significant figures for , Give the answer to the correct number of significant figures: 1.
Algebraic Manipulation. Scientific Notation. Manipulation of Exponents. Dimensional Analysis. The Quadratic Equation.
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