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NIS - PHYSICS

NIS - PHYSICS. Lecture 2 Significant Figures , Scientific Notation and SI System Ozgur Unal. Significant Figures. 31.49 has 4 significant figures 167 has three significant figures 28 has two significant figures with zeroes , things get complicated.

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NIS - PHYSICS

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  1. NIS - PHYSICS Lecture 2 SignificantFigures, ScientificNotation and SI System OzgurUnal

  2. Significant Figures • 31.49 has 4 significantfigures • 167 has threesignificantfigures • 28 has twosignificantfigures withzeroes, thingsgetcomplicated.. The number of reliably known digits in a number is called the number of significant figures.

  3. Significant Figures Zeroes placed before other digits are not significant; 0.046 has two significant digits. Zeroes placed between other digits are always significant; 4009 kg has four significant digits. The followings are the rules to find the significant figures when zeroes are involved: Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.

  4. Significant Figures Zeroes at the end of a number are significant only if they are behind a decimal point as in (3). Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point: 8.200 x 10^3 has four significant digits 8.20 x 10^3 has three significant digits 8.2 x 10^3 has two significant digits

  5. Scientific Notation • Scientificnotationallowsthenumber of significantfiguresto be clearlyexpressed. • Ithelpswriteextremenumberseasily. • Try: 0.00000338  ? 6,392,000  ? We commonly write numbers in “powers of ten” or scientific notation. For example: 36,900  3.69 x 10^4 0.0021  2.1 x 10^-3

  6.  3 significant figures Significant Figures - Exercises • 0.019  2 significant figures • 60,086  5 significant figures • 0.00109  3 significant figures • 19.00  4 significant figures 341 • 270  ? significant figures • 27 x 10^1 • 2.70 x 10^2  2 significant figures  3 significant figures

  7. Significant Figures • When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted. 3.6 – 0.57 = 3.0 In multiplication, division, trigonometric functions, etc., the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc. 11.3 cm * 6.8 cm = 77 cm^2

  8. Significant Figures The Two Greatest Sins Regarding Significant Digits Writing more digits in an answer than justified by the number of digits in the data. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer. • ab/c = ?, where a = 483, b = 73.67, and c = 15.67 • x + y + z = ?, where x = 48.1, y = 77, and z = 65.789

  9. Unıts Standards and the SI System The measurement of any quantity is made relative to a particular standard or unit. The length of an object is 2.3  meaningless Meter, second, kg, Kelvin etc. Standard defines how long one meter or one second or any other unit is. • Length: Standard unit of length is meter (m). • Time: Standar unit of time is second (s). • Mass: Standard unit of mass is kilogram (kg).

  10. UnitsStandardsandthe SI System Unit prefixes:

  11. Unıts Standards and the SI System • Base vs Derived Units: A base unit must be defined in terms of a standard. System of Units: We need consistent set of units. Why? SI units: m – kg - s Cgs System: cm – g - s British Engineering System: foot – pound - s Allotherunitsarederivedfrombaseunits. Forexample: unit of speed (m/s), unit of energy (Joule)

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