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NIS - PHYSICSNIS - PHYSICS

Lecture 2Lecture 2

Significant Figures, Scientific Significant Figures, Scientific Notation Notation

and SI Systemand SI System

Ozgur UnalOzgur Unal

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Significant FiguresSignificant FiguresThe number of reliably known digits in The number of reliably known digits in a number is called the number of a number is called the number of significant figuressignificant figures..

31.49 has 4 significant figures31.49 has 4 significant figures167 has three significant figures167 has three significant figures28 has two significant figures28 has two significant figures

with zeroes, things get complicated..with zeroes, things get complicated..

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Significant FiguresSignificant FiguresThe followings are the rules to find the The followings are the rules to find the significant figures when zeroes are significant figures when zeroes are involved:involved:1.1. Zeroes placed before other digits are Zeroes placed before other digits are

not significant; 0.046 has two not significant; 0.046 has two significant digits. significant digits.

2.2. Zeroes placed between other digits Zeroes placed between other digits are always significant; 4009 kg has are always significant; 4009 kg has four significant digits. four significant digits.

3.3. Zeroes placed after other digits but Zeroes placed after other digits but behind a decimal point are behind a decimal point are significant; 7.90 has three significant significant; 7.90 has three significant digits. digits.

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Significant FiguresSignificant Figures4.4. Zeroes at the end of a number are Zeroes at the end of a number are

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

8.20 x 10^3 has three significant digits 8.20 x 10^3 has three significant digits

8.2 x 10^3 has two significant digits8.2 x 10^3 has two significant digits

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Scientific NotationScientific NotationWe commonly write numbers in “powers We commonly write numbers in “powers of ten” or scientific notation.of ten” or scientific notation.

For example: 36,900 For example: 36,900 3.69 x 3.69 x 10^410^4

0.0021 0.0021 2.1 x 10^-3 2.1 x 10^-3Scientific notation allows the number of Scientific notation allows the number of significant figures to be clearly significant figures to be clearly expressed.expressed.It helps write extreme numbers easily.It helps write extreme numbers easily.Try:Try: 0.00000338 0.00000338 ? ?

6,392,000 6,392,000 ? ?

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Significant Figures - ExercisesSignificant Figures - Exercises341341 3 significant figures3 significant figures0.0190.019 2 significant figures2 significant figures60,08660,086 5 significant figures5 significant figures0.001090.00109 3 significant figures3 significant figures19.0019.00 4 significant figures4 significant figures

270270 ? significant figures? significant figures

2 significant figures2 significant figures 3 significant figures3 significant figures

27 x 10^127 x 10^12.70 x 10^22.70 x 10^2

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Significant FiguresSignificant FiguresIn multiplication, division, trigonometric In multiplication, division, trigonometric functions, etc., the number of significant functions, etc., the number of significant digits in an answer should equal the least digits in an answer should equal the least number of significant digits in any one of number of significant digits in any one of the numbers being multiplied, divided the numbers being multiplied, divided etc. etc.

11.3 cm * 6.8 cm = 77 cm^211.3 cm * 6.8 cm = 77 cm^2When quantities are being added or When quantities are being added or subtracted, the number of subtracted, the number of decimal places decimal places (not significant digits) in the answer (not significant digits) in the answer should be the same as the least number should be the same as the least number of decimal places in any of the numbers of decimal places in any of the numbers being added or subtracted. being added or subtracted.

3.6 – 0.57 = 3.03.6 – 0.57 = 3.0

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Significant FiguresSignificant FiguresThe Two Greatest Sins Regarding The Two Greatest Sins Regarding Significant Digits Significant Digits Writing more digits in an answer than Writing more digits in an answer than justified by the number of digits in the justified by the number of digits in the data. data. Rounding-off, say, to two digits in an Rounding-off, say, to two digits in an intermediate answer, and then writing intermediate answer, and then writing three digits in the final answer. three digits in the final answer.

ab/c = ?, where a = 483, b = 73.67, and c ab/c = ?, where a = 483, b = 73.67, and c = 15.67 = 15.67

x + y + z = ?, where x = 48.1, y = 77, and x + y + z = ?, where x = 48.1, y = 77, and z = 65.789 z = 65.789

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Unıts Standards and the SI Unıts Standards and the SI SystemSystem

The measurement of any quantity is The measurement of any quantity is made relative to a particular standard or made relative to a particular standard or unitunit..The length of an object is 2.3 The length of an object is 2.3 meaninglessmeaninglessMeter, second, kg, Kelvin etc.Meter, second, kg, Kelvin etc.Standard Standard defines how long one meter or defines how long one meter or one second or any other unit is.one second or any other unit is.Length: Length: Standard unit of length is meter Standard unit of length is meter (m).(m).Time:Time: Standar unit of time is second (s). Standar unit of time is second (s).Mass: Mass: Standard unit of mass is kilogram Standard unit of mass is kilogram (kg).(kg).

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Units Standards and the SI Units Standards and the SI SystemSystem

Unit prefixes:Unit prefixes:

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Unıts Standards and the SI Unıts Standards and the SI SystemSystem

System of Units: System of Units: We need consistent set We need consistent set of units. Why?of units. Why?

SI units: SI units: m – kg - sm – kg - sCgs System: Cgs System: cm – g - scm – g - sBritish Engineering System: British Engineering System: foot – pound - sfoot – pound - s

Base vs Derived Units:Base vs Derived Units:

A base unit must be defined in A base unit must be defined in terms of a standard. terms of a standard.

All other units are All other units are derived derived from from base units. For example: unit of speed base units. For example: unit of speed (m/s), unit of energy (Joule)(m/s), unit of energy (Joule)