Unit, Dimension and Errors is an important topic in Physics. Some questions are asked directly from this topic. Most importantly, the whole of physics includes this topic. So, it is very important to have a clear idea about this. These study notes on Units, Dimensions and Measurements will help you to read next chapters in the subject
Units, Dimensions and Measurements
To quantify or express a quantity we need a standard of measurement. This standard is known as a unit of measure.
To measure any quantity, we need two things = numerical value (n) × unit (u) required
Basic Units: The units for basic or basic quantities are called basic or basic units.
Base Units: All other units of quantity can be expressed as combinations of base units.
International System of Units
Following are some measurement systems that are used.
CGS system- This system of units has centimeter as unit of length, gram as unit of mass and second as unit of time.
FPS System – This system of units uses feet as the unit of length, pounds as the unit of mass and seconds as the unit of time.
MKS System- This system of units has meter as unit of length, kilogram as unit of mass and second as unit of time.
Currently, the internationally accepted unit system for measurement is (SI System – International System of Units). It is similar to the MKS system.
SI quantities and units
Accuracy, precision, and error of measurement
Accuracy- refers to the precision of a measurement. That is, a measure of how close the measured value is to the true value of the quantity. It depends on the number of significant figures in it. The larger the significant figure, the greater the precision.
Precision – Precision is the degree of accuracy. It depends on the minimum count of the measuring instrument. The lower the minimum count, the more precise the measurement.
error
The uncertainty of a measurement is called error. Every calculated quantity based on measured values also has an error.
Error in measurement can be classified as (1) systematic error and (2) random error.
Systematic error: Systematic error is due to errors in measuring instruments, test design, or imperfect methods of observation. These errors can be reduced by improving the experimental conditions, using a different method or different equipment, repeating the measurement.
Random Error: Random error is the error that occurs due to random and unpredictable causes in the experimental conditions, such as personal error by the observer. These errors can be minimized by conducting repeated trials using proper equipment.
Significant figures
The significant figure indicates the precision of the measurement that depends on the minimum count of the measuring instrument.
Rules for significant figures
All non-zero numbers are significant.
All zeros between two non-zero numbers are significant, regardless of where the decimal point is.
If the number is less than 1, the zeros to the right of the decimal point, but to the left of the first non-zero digit, are not significant. Ex: In 00532, zero before digit 5 is not significant
A terminal zero of a number without a decimal point is not significant.
For example 45200 cm = 452 meters has three significant figures.
Regression between a number with a decimal point is zero significant. For example, 54.500 has five significant figures.
The magnitude of different sums
The magnitude of an expression can be defined as the number of times the base expressions are raised to represent that expression. All amounts can be expressed in terms of base amounts.
