Revision: Class 11 >> Units and Measurement NEET (UG) Units and Measurement

One metre is defined as the distance travelled by light in the air in  `1/(299,792,458)` of a second.

The S. I. unit of length is meter.

Multiple of metre = Kilometre (km).

Submultiple of metre = Centimetre (cm)

The density of a substance is defined as the mass of a unit volume of that substance.

`"Density" = "Mass"/"Volume"`

Mass is the amount of matter contained in a body. Its unit is a kilogram (kg).

Random errors are unpredictable fluctuations in measurements that vary in both magnitude and direction. 

When relative error is represented as percentage it is called the percentage error.

Percentage error = `(triangle"a"_"mean")/("a"_"mean") xx 100`

Systematic errors are consistent deviations from the true value caused by flaws in the measurement system.

When a physical quantity is measured incorrectly, it can result in an error.

The ratio of the mean absolute error in the measurement of a physical quantity to its arithmetic mean value is called relative error.

Relative error = `(triangle "a"_"mean")/"a"_"mean"`

For a given set of measurements of the same quantity, the arithmetic mean of all the absolute errors is called mean absolute error in the measurement of that physical quantity.

`triangle "a"_"mean" = (triangle"a"_1 + triangle"a"_2 + ......+ triangle"a"_"n")/"n" = 1/"n"` \[\sum_{i=1}^n\triangle a_i\]

1. For a given set of measurements of a quantity, the magnitude of the difference between mean value (Most probable value) and each individual value is called absolute error (Δa) in the measurement of that quantity.
2. absolute error = |mean value - measured value|
   Δa₁ = |a_mean - a₁|
   Similarly,
   Δa₂ = |a_mean - a₂|,
             `\vdots           \vdots             \vdots`
   Δa_n = |a_mean - a_n|