Measurement of Length: Ruler,Measuring Tape, Vernier Caliper, Screw Gauge

Here you can some common tools for measuring length.

Longest lengths are measured through measuring tape, then goes the ruler scale and then the vernier caliper and screw gauge for small to minute as well as accurate measurement. 

However, physical measurement involves error and every physical measurement is an approximation.

Accuracy and Precision
The most meaningful way of interpreting a measurement is as an interval with a lower bound and an upper bound. Imagine that we have measured a line segment, using a ruler divided into centimeters, and found the length to be 5 cm. 
To be more precise, we can state the measure as an interval -- either in words, 5 cm to the nearest 0.5 cm, or using notation, such as 5 cm±0.5 cm (5±  0.5 implies a lower bound of 4.5 and an upper bound of 5.5). We can also state that the maximum possible error for this measure is 0.5 cm.the precision of a measurement depends on the size of the smallest measuring unit.. The smaller the interval, the more we have "narrowed it down," and thus the more precise the measurement.

Scientific Notation and Prefixes for SI Units

The numerical values of basic or derived in SI units maybe too big or too small in comparison with each other. They are well expressed using Scientific notation, also known as standard form. This is expressed as:

                                                                   M x 10ⁿ

^where

•   M is the coefficient  1<M<10
•  10 is the base
•  n is the exponent or power of 10

For example when we say that a star is 8 x 10⁹km from Earth means, it is 8000,000,000 km from Earth.

SI Unit Prefixes for Length

NAME	PREFIX	SYMBOL	FACTOR
gigameter	giga	Gm	109
megameter	mega	Mm	106
kilometer	kilo	km	103
decimeter	deci	dm	10-1
centimeter	centi	cm	10-2
millimeter	milli	mm	10-3
micrometer	micro	μm	10-6
nanometer	nano	nm	10-9
picometer	pico	pm	10-12

Measurements

Correct Measurement of quantities is the first and the most important step in all sciences especially Physics.Quantities must be described after careful observation, repeated experiments and accurate measurements. No fact in science is accepted and no law can be formed till it is bad on exact measurements.

Quantities that can be measured: 

Mass, Weight, Time, Length, Volume and many more.( Physical Quantities)

How they can be measured:

Through various measuring devices such as

• Mass by Beam Balance, Electronic Balance or Spring Balance,
• Weight by calibration of Spring Balance,
• Time by Clocks, Watches or Pendulums,
•  Length by Measuring Tape, Meter rule, Vernier Caliper or Screw Gauge,
• Volume by Measuring cylinders, calibrated test tubes etc.

 and so on.

Physical Quantities may be Basic or Derived.

Basic Quantities are Length, Mass, Time, Force, Current, and Temperature. These have units of their own origin, not from anything. (metre, kg, second, Newton, Ampere, Kelvin).

Derived  Quantities are those whose units are derived from some basic quantity, such as Moment and Speed, whose units are Newton-metre and metre per second, respectively.

 

A Physical Quantity has two parts, numerical magnitude and unit

If for example we talk of a length of 85 m, 

85 is the numerical magnitude while metre is the unit, whose symbol is m.

You tell

Physical Quantity	Numerical Magnitude	Unit	Symbol
Length:  7 km
Mass:  400 mg
Time:      22 seconds
Length: 8 cm
Mass: 5 kg
Time: 3 hours

In this you must have noticed that there are different units for the same physical quantity. This is a problem! There should be a standard. So the scientists have devised many standards over time, calling them system of units. In past there were FPS (foot, pound, second) , CGS (centimeter, gram, second) and MKS (metre, kilogram, second) systems.

 The MKS system is further modified into SI or System International, which is what we follow today.  The units of this are called SI units.

SI units of length mass and time are meter, kilogram and second. SI units of various basic and derived quantities are standardized (and found in various books, not here)