SI units interpolation extrapolation | Study notes Chemistry

The International System of Units (Systeme Internationale

d'Unites); interconversion of SI and metric units

Metric units, which are often not identical to the latest international standards, are widely

used among chemists and physicists around the world to record the results of their measurements.

The basic metric units of length, mass, and volume are meter, gram and liter. When smaller or

larger units are needed a system based on the powers of ten is used to form prefixes. The SI system

of units is a modern and internationally accepted version of the metric system. In the SI system,

the relationship between the different fundamental units is rigorously consistent. The main

advantage of the SI system is that its exclusive use during calculations guarantees that any

intermediate or final results for both fundamental and derived quantities will also be obtained in

SI units without the need for conversion factors.

The following table gives the metric and SI units of the most important physical quantities.

Physical property SI unit Metric unit Conversion

Length meter (m) meter (m)

Volume cubic meter (m3) liter (l) 1 l = 10–3 m3 = 1 dm3

Mass kilogram (kg) gram (g) 1 kg = 103 g

Pressure pascal (Pa) atmosphere (atm) 1 Pa = 1 N/m2

1 atm = 101325 Pa

torr (mmHg) 1 torr = 1.333102 Pa

bar 1 bar = 105 Pa

Temperature kelvin (K) Celsius degree (oC) K = 273.15 + oC

Energy joule (J) calorie (cal) 1 cal = 4.184 J

Significant Figures

In science, it is fundamentally important to indicate the accuracy of measured or calculated

data. The primary way of indication is to control the number of significant figures of a quantity.

To do this, it is convenient to give all numbers in the common scientific notation using a factor

between 1 and 10 multiplied by the appropriate power of 10. The number of digits in the first factor

is the number of significant figures. For example:

40200 = 4.02  104 : the number of significant figures is three

The number of significant figures in any given quantity can be determined as follows:

(a) If there is no decimal point in the number, a count of the digits from the first non-zero digit on

the right to the last non-zero digit on the left gives the number of significant figures.

(b) If the number contains a decimal point, a count of the digits from the first non-zero digit on the

left to the very last digit (regardless of its value) on the right gives the number of significant figures.

Partial preview of the text

Download SI units interpolation extrapolation and more Study notes Chemistry in PDF only on Docsity!

The International System of Units (Systeme Internationale

d'Unites); interconversion of SI and metric units

Metric units, which are often not identical to the latest international standards, are widely used among chemists and physicists around the world to record the results of their measurements. The basic metric units of length, mass, and volume are meter, gram and liter. When smaller or larger units are needed a system based on the powers of ten is used to form prefixes. The SI system of units is a modern and internationally accepted version of the metric system. In the SI system, the relationship between the different fundamental units is rigorously consistent. The main advantage of the SI system is that its exclusive use during calculations guarantees that any intermediate or final results for both fundamental and derived quantities will also be obtained in SI units without the need for conversion factors. The following table gives the metric and SI units of the most important physical quantities.

Physical property SI unit Metric unit Conversion

Length meter (m) meter (m) Volume cubic meter (m^3 ) liter (l) 1 l = 10–^3 m^3 = 1 dm^3 Mass kilogram (kg) gram (g) 1 kg = 10^3 g Pressure pascal (Pa) atmosphere (atm) 1 Pa = 1 N/m^2 1 atm = 101325 Pa torr (mmHg) 1 torr = 1.333 102 Pa bar 1 bar = 10^5 Pa Temperature kelvin (K) Celsius degree (oC) K = 273.15 + oC Energy joule (J) calorie (cal) 1 cal = 4.184 J

Significant Figures

In science, it is fundamentally important to indicate the accuracy of measured or calculated data. The primary way of indication is to control the number of significant figures of a quantity. To do this, it is convenient to give all numbers in the common scientific notation using a factor between 1 and 10 multiplied by the appropriate power of 10. The number of digits in the first factor is the number of significant figures. For example: 40200 = 4.02  104 : the number of significant figures is three The number of significant figures in any given quantity can be determined as follows: (a) If there is no decimal point in the number, a count of the digits from the first non-zero digit on the right to the last non-zero digit on the left gives the number of significant figures. (b) If the number contains a decimal point, a count of the digits from the first non-zero digit on the left to the very last digit (regardless of its value) on the right gives the number of significant figures.

Examples:

Significant figures Significant figures 5270 3 0.320 3 5027 4 0.32 2 0.0129 3 10.01 4

There are simple rules for giving significant figures in values calculated by mathematical operations. For multiplication or division the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. For addition or subtraction the result has the same number of decimal places as the least precise measurement in the calculation.

Accuracy and precision

Scientific measurements almost always have some error. This error may result from the limitation of the instruments used or the limitations of human senses. It is exceptionally rare to find that an experimentally measured value is exactly the same as theoretical predictions. The term accuracy is used to refer to the closeness of single measurement to the true value. The smaller the difference between the experimental and theoretical value the more accurate the results and the measuring device are. Some devices are more accurate than others. For example, 10 cm^3 of a liquid can be both measured by a single-volume pipette or a measuring cylinder. Pipettes are more accurate in this comparison. However, the true value is only known if some kind of standard can be used for comparison. For most measurements, the true or theoretically predicted value is not known. This is why before the first use of any measuring device calibration must be done. This calibration is always in comparison with some kind of standard and makes sure that the new device is accurate enough. After careful calibration, the device can be trusted in further measurements. Errors in measurements are almost always unavoidable. The best option for scientists to decrease the error of results is to do the same measurement several times (called parallel measurements) and calculate the average. The average is always more reliable than the result of a single measurement. For really reliable measurements, the parallel results are close to each other. Precision is used to refer to the closeness of the set of values obtained from identical measurements of a quantity on the same instrument. Precision is often given numerically as mean deviation. To

obtain mean deviation, first the mean value has to be calculated ( x ), the absolute values of the

individual deviations must be summed (  x - x =i   i 0), and finally divided by the number of

identical measurements ( = 

^ i ).

SI units interpolation extrapolation, Study notes of Chemistry

Related documents

Partial preview of the text

Download SI units interpolation extrapolation and more Study notes Chemistry in PDF only on Docsity!

The International System of Units (Systeme Internationale

d'Unites); interconversion of SI and metric units

Significant Figures

Accuracy and precision

individual deviations must be summed (  x - x =i   i 0), and finally divided by the number of

identical measurements ( = 