The Science Portal: 21C Science with Style

tells us how close the measured value of a quantity is to its true value. An accurate measurement is "close" to a true value. An inaccurate measurement is "far" from a true value.

are not fundamental but can be expressed in terms of fundamental units.

are the most basic units which cannot be expressed in terms of other units. The seven fundamental units are
1. meter (m);
2. second (s);
3. kilogram (kg);
4. Kelvin (K);
5. The Ampere (A);
6. mole (mol);
7. candela (cd).

are used to find the value of the exponent $n$ and coefficient $a$ for the general relationship $y= a x^n$.
The value of the gradient for the log-log plot equals $n$ and $a= log^{-1}{(\text{y-intercept})}$.
For example
A linear relationship should have $n \approx 1$;
A square-root relationship should have $n \approx \frac{1}{2}$;
A quadratic relationship should have value $n \approx 2$;
An inverse-square relationship should have value $n \approx -2$.

tells us how consistent repeated measurements are. A precise set of measurements are relatively closer together. An imprecise set of measurements are spread apart.

$y \propto x$ or $y = m x$, occurs when the relationship between $y$ and $x$ is linear with a zero y-intercept value, that is, a straight line passing through the origin.
The x- and y-error bars may allow a range of values for the y-intercept, because the lines of max & min gradients, thus showing a possible proportional relationship for a best-fit straight line even if its y-intercept value is non-zero. Beware, for the IB, a best-fit line can be any curve which fits the data points. It does not mean the best-fit straight line.

is a fluctuating error often present in experiments. It is linked to precision: imprecise data => "high" random error; precise data => "low" random error. Repeated measurements do reduce random errors. Sources of random errors can include varying reading/human error and other randomly flucuating factors which cannot be controlled during experiments.

of vectors, changes the magnitude of the vector but not the direction.
For scalar $a$ and vector $\vec{A}$ with
x- or horizontal component $A_H=A \cos \theta$
y- or vertical compnonet $A_V= A \sin \theta$
magnitude $A=\sqrt{A_H^2 + A_V^2}$

The multiplication $a \times \vec{A}$ has magnitude $a \times A$.
The division $\vec{A} \div a$ has magnitude $A \div a$.

have magnitude only. Direction or changes in direction have no effect on scalar quantities. Examples include distance, speed, mass and temperature.

a rule, the number of significant digits in a result should not exceed that
of the least precise value upon which it depends.