SI Units and Significant Figures

Study Notes

International System of Units (SI) is a standardized system of measurement used globally
Seven base units:
1. Meter (m) - length
2. Kilogram (kg) - mass
3. Second (s) - time
4. Ampere (A) - electric current
5. Kelvin (K) - temperature
6. Mole (mol) - amount of substance
7. Candela (cd) - luminous intensity
Derived units are formed by combining base units, e.g. velocity (m/s), force (N = kg m/s²)

Significant figures (sig figs) represent the precision of a measurement
Rules for sig figs:
- Non-zero digits and trailing zeros in a number with a decimal point are significant
- Leading zeros are not significant
- Zeros between non-zero digits are significant
Operations with sig figs:
- Addition and subtraction: result has the same number of sig figs as the number with the fewest sig figs
- Multiplication and division: result has the same number of sig figs as the number with the fewest sig figs

Types of errors:
- Systematic errors: consistent and repeatable, e.g. faulty instrument
- Random errors: unpredictable and vary in magnitude, e.g. human error
- Absolute error: difference between measured value and true value
- Relative error: ratio of absolute error to true value
Percent error: relative error expressed as a percentage

Conversion between units involves replacing one unit with an equivalent unit
Conversion factors: ratios of equivalent units, e.g. 1 inch = 2.54 centimeters
Conversion steps:
1. Identify the units to be converted from and to
2. Write the conversion factor
3. Multiply the original value by the conversion factor

Dimensional analysis: a method for converting between units by canceling out unwanted dimensions
Steps for dimensional analysis:
1. Write the conversion factor as a fraction
2. Cancel out unwanted dimensions by multiplying by the conversion factor
3. Simplify the resulting expression
Dimensional analysis can be used to convert between different units and to solve problems involving multiple conversions.

International System of Units (SI) is a globally accepted standardized system of measurement
Seven base units in SI, each represents a fundamental physical quantity
Meter (m) - unit of length
Kilogram (kg) - unit of mass
Second (s) - unit of time
Ampere (A) - unit of electric current
Kelvin (K) - unit of temperature
Mole (mol) - unit of amount of substance
Candela (cd) - unit of luminous intensity
Derived units are formed by combining base units, examples include velocity (m/s) and force (N = kg m/s²)

Significant figures (sig figs) represent the precision of a measurement
Non-zero digits and trailing zeros in a number with a decimal point are significant
Leading zeros are not significant, and zeros between non-zero digits are significant
When performing operations with sig figs, the result has the same number of sig figs as the number with the fewest sig figs
Rules for sig figs apply to addition, subtraction, multiplication, and division operations

Errors in measurement can be systematic, random, or a combination of both
Systematic errors are consistent and repeatable, often due to faulty instruments
Random errors are unpredictable and vary in magnitude, often due to human error
Absolute error is the difference between a measured value and the true value
Relative error is the ratio of absolute error to the true value, often expressed as a percentage
Percent error is a measure of relative error expressed as a percentage

Conversion between units involves replacing one unit with an equivalent unit
Conversion factors are ratios of equivalent units, such as 1 inch = 2.54 centimeters
Conversion steps involve identifying the units to be converted from and to, writing the conversion factor, and multiplying the original value by the conversion factor
Conversion factors can be used to simplify complex conversions and reduce errors

Dimensional analysis is a method for converting between units by canceling out unwanted dimensions
Dimensional analysis involves writing the conversion factor as a fraction and canceling out unwanted dimensions by multiplying by the conversion factor
Steps for dimensional analysis include writing the conversion factor, canceling out unwanted dimensions, and simplifying the resulting expression
Dimensional analysis can be used to solve problems involving multiple conversions and to simplify complex calculations