Measurement always have Uncertainties. If we measure the thickness of a text book using ordinary ruler is different if we use the micrometer caliper.
Thickness of book (ordinary ruler) = 30 ± 1 mm
Thickness of book (micrometer caliper) = 30.00 ±0.01 mm
The accuracy of measurement – how close measured value to the true value. The symbol ± and a second number indicating the uncertainty of the measurement.
If the diameter of a steel rod is given as 56.47 ± 0.02 mm, this means that the true value is unlikely less than 56.45 mm or greater than 56.49 mm.
In a commonly used shorthand notation, the number 1.6454 (21) means 1.6454 ± 0.0021.
Fractional error or percent error – maximum.
Example : A resistor labeled “ 47 Ohms ±10%” – has true resistance that differs from 47 Ohms by no more than 10% of 47 Ohms – that is about 5 Ohms. The resistance is probably between 42-52 Ohms.
Example: The diamter of steel rod given above, the fractional error is 0.02mm/56.57 mm – about 0.004, the percent is (0.0004)(100%) – 0.04%.
Significant figure: the number of meaning digits in the measured value.
Example: the thickness of the book is 3.21 mm – has three significant figure. By this we mean that the first two digits are known to be correct,while the third digit is uncertain.
Example: the distance from KL to JB is 350 km. Also has three significant figure, but uncertainty is about 1 km.
When you use number having uncertainties to compute other numbers, the number computed numbers are also uncertain.
Multiplied or divided – the number of significant figures in the result can be no greater than in the factor with the fewest of significant figure.
Example: 3.1416 x 2.34 x 0.58 = 4.3
Add or subtract – its the location of the decimal point that maters, not the number of significant figure.
Example: 123.62 + 8.9 = 132.5
