SCIENTIFIC NOTATION

SCIENTIFIC NOTATION

Numbers are expressed in standard form called scientific notation which uses power of ten.

The internationally accepted practice is that there should be only one non-zero digit left of decimal. For example the number 134.7 can be written as 134.7 = 1.347 x 10²

Similarly 0.0023 can be written as 0.0023 = 2.3 x 10^-3

Use of prefix:

Prefixes are used to express these large or small numbers as multiple of ten. For example

1 light year = 946 x 10¹³m = 9.46 x 10¹⁵m

Similarly for smaller number Radius of proton = 12 x 10^-16 m = 1.2 x 10^-15 m

CONVENTIONS FOR INDICATING UNITS:

Uses of SI units require special care, especially in writing prefixes. Following points should be kept in mind during the uses of units.

i)              Full name of the unit does not begin with a capital letter even if named after a scientist e.g. newton.

ii)             The symbol of unit named after a scientist has initial capital letter such as N for newton.   

iii)           The prefix should be written before the unit without any space; such as 1 x 10^-3 m is written as 1 mm. Standard prefixes are given in the following table.

Factor	Prefix	Symbol
10-18	atto	a
10-15	femto	f
10-12	pico	p
10-9	nano	n
10-6	micro	µ
10-3	milli	m
10-2	centi	c
10-1	deci	d
101	deca	da
103	kilo	k
106	mega	M
109	giga	G
1012	tera	T
1015	peta	P
1018	exa	E

iv)           A combination of base units is written each with one space apart. For example, newton meter is written as Nm.

v)            Compound prefixes are not allowed. For example, 1 µµF may be written as 1pF.

vi)           A number such as 5.0 x 10⁴ cm may be expressed in scientific notation as 5.0 x 10² m

vii)         When a multiple of a base unit is raised to a power, the power applies to the whole multiple and not the base unit alone. Thus 1km² = 1 (km)² = 1 x 10⁶ m²

viii)        Measurement in practical work should be recorded immediately in the most convenient unit e.g. micrometer screw gauge measurement in mm and the mass of the calorimeter in grams (g). But before calculation for the result, all measurements must be converted to the appropriate SI base units.