Measurement
Table of Contents
Types
Metric System
Metric Prefix
- The General Conference on Weights and Measures recommends the following use of prefixes:
- Rules
- The prefix is combined with the unit of measurement.
- Ex: kilogram (kg), kilowatt (kW).
- All of the prefix symbols are made from upper- and lower-case Latin except for micro.
- SI units and unit symbols are never show in italics. The prefixes and symbols following that are always prefixed without any space or punctuation.
- Ex: 'ms' means millisecond
- 'm s' or 'm·s' means metre second
- Prefixes up to power of 1000 are preferred rather than let's say tens (deci-, deca-) and hundreds (cent-, hecto-).
- Prefixes cannot be used in combination on a single unit.
- Ex: (mg) milligram instead of microkilogram (μkg).
- The units are treated as multiplicative factors to values and the prefixes as 10x multiplier.
- A prefix symbol attached to a unit symbol is included when the unit is raised to a power.
- Ex: km^2 is km x km, not km x m
- or you look at this as (km)^2 and not k(m)^2
- The prefix is combined with the unit of measurement.
- SI Prefix Table
Prefix Symbol Base-10 Adoption quetta Q \(10^{30}\) 2022 ronna R \(10^{27}\) 2022 yotta Y \(10^{24}\) 1991 zetta Z \(10^{21}\) 1991 exa E \(10^{18}\) 1975 peta P \(10^{15}\) 1975 tera T \(10^{12}\) 1960 giga G \(10^{9}\) 1960 mega M \(10^{6}\) 1873 kilo k \(10^{3}\) 1795 hecto h \(10^{2}\) 1795 deca da \(10^{1}\) 1795 deci d \(10^{-1}\) 1795 centi c \(10^{-2}\) 1795 milli m \(10^{-3}\) 1795 micro μ \(10^{-6}\) 1873 nano n \(10^{-9}\) 1960 pico p \(10^{-12}\) 1960 femto f \(10^{-15}\) 1964 atto a \(10^{-18}\) 1964 zepto z \(10^{-21}\) 1991 yocto y \(10^{-24}\) 1991 ronto r \(10^{-27}\) 1991 quecto q \(10^{-30}\) 2022 - Facts
- The first use of prefixes in SI units date back to the definition of kilogram after the French Revolution.
- The adoption of ronna- and queta- was proposed by British metrologist Richard J. C. Brown.
English System
FPS System
- Known as foot-pound-second system.
- Built around three fundamental units: foot for length, pound for mass/force, second for time.
Significant Figures
- We are only limited by the precision of the instrument when measuring.
- Ex: We can only estimate 2.33cm but not 2.33481cm.
Rules for determining
- Non-zero digits are significant.
- 316 -> 3 significant figures.
- Zeroes in between other non-zero digits are significant.
- 6.003 -> 4 significant figures
- Leading zeroes are not significant. -> 0.00035 = 2 significant figures
- Trailing decimal zeroes are significant.
- 35,000 -> 2 significant figures
- 0.035000 -> 5 significant figures
Rules when calculating
ALWAYS the least.
- When adding or subtracting, use the fewest number of decimal places.
10.1 -> 1 decimal place \+ 7.43 -> 2 decimal places --------- 17.5 -> 1 decimal place
- When multiplying or dividing, use the fewest number of significant figures.
4.93 -> 3 significant figures x 6.027 -> 4 significant figures --------- 29.7 -> 3 significant figures
Accuracy vs Precision
Accuracy
- Closeness to true value.
- This is when you know the exact value of what you're trying to measure and the result of the experiment is close to the exact value.
- It describes how well the results agree with an accepted value of the quantity being measured.
Precision
- Closeness of a set of data points to one another.
- It refers to the degree of exactness to which a measurement can be reproduced.
Scalar
- a quantity that describes by magnitude only.
- Examples include:
- time
- length
- speed
- temperature
- mass
- energy