A quantitative comparison of an object's physical quantity that involves a number and a unit
Unit
The magnitude of a physical quantity and may vary as a standard or non-standard unit
Metric System
Based upon the power of ten to express a very large or very small number
Base Units
Meter - length
Gram - mass
Liter - volume
SI (Systeme International) unit
Based on the metric system but has 7 fundamental units
Each prefix of the International System of units denotes a decimal number in a measurement expressed in the power of ten
For example, in mg; milli is the prefix used to denote the magnitude of the unit and gram is the base unit
7 SI Fundamental Units
Mass: Gram: g
Electric Current: Ampere: A
Temperature: Kelvin: K
Time: Second: s
Amount of Substance: Mole: mol
Length: Meter: m
Luminous Intensity: Candela: CD
Scientific Notation
A simplified expression for a very large or very small number or quantity
Standard form of scientific notation
A x 10^b
Expressing LARGE Numbers in Scientific Notation
1. Move the decimal point to the LEFT
2. The number of times the decimal point is moved indicates the decrease or increase in the exponent
3. The exponent is positive when expressing large numbers
Expressing SMALL Numbers in Scientific Notation
1. Move the decimal point to the RIGHT
2. The exponent is negative when expressing smaller numbers
Conversion Factor
A mathematical statement of two equivalent measurements of different units that can be expressed in fraction form
Ratio which represents the relationship between two units
Always equal to one
Accurate
Capable of providing a correct reading or measurement
Accuracy
A measure of how close a measurement comes to the actual or true value of what's being measured
How close you are to the accepted value
Precision
The degree of consistency and agreement among independent measurements of the same quantity for the reliability of results
A measure of how close a series of measurement are to one another
How carefully measurements were made
If the true value is not given, get the average of the series of measurements then compare
Determining Error
Error = Ev - Av
Experimental value (ev)
Is measured in the lab
Accepted Value (av)
Is the correct or true value based on reliable references
Error
Is the difference between the ev and av
Percent Error
Percent Error = (Ev- Av) / Av (100)
The percent error is an absolute value (no positive/ negative)
The acceptable percent of error is +/- 5%
Significant Figures
Each of the digits of a number that are used to express it to the required degree of accuracy and precision
Digits that convey precision with which a number is known
Rules in Determining Significant Figures
All nonzeroes are significant
Zeroes between nonzeroes are significant
Leading zeroes (zeroes from the left of a nonzero) are not significant
Trailing zeroes (zeroes after the nonzero) are significant
Every digit in a scientific notation is significant
Final Zeroes may or may not be significant - significant if behind a decimal point, otherwise if after a decimal point, drawing a bar on top of the zeroes could make it significant
Rounding-off Numbers
A value is raised or lowered to a much more precise number
Rounding Rules
If the digit is greater than 5, addone then drop all the digits
If the digit to be dropped is less than 5, drop it without adding anything
If the digit is exactly 5 and the digit to be retained (left of 5) is even, then just drop the5
If the digit to be retained is odd, then add one and drop
Addition and Subtraction
1. The number of decimal places in the final answer should be equal to the smallest number of decimal places
2. The answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places
Multiplication and Division
1. The significant figures and not the decimal places
2. The final answer cannot contain more significant figures than those in the least accurate measurement
Mixed Operations
1. When multiple operations are used, evaluate the ones inside the parenthesis then round it to the number of significant figures
2. Use the rounded number to proceed to the next operation