Standard type of number. Actions with numbers in standard form

Standard form (normalized notation)

The standard (normalized) form of a positive number is written as a product:

a\cdot10^n,

where $1\leq a<10$ (the mantissa) and

n

is an integer (the exponent of ten, the "order" of the number). For negative numbers, factor out the sign, then write

|x|

in standard form:

{-}\,b\cdot10^n

with

1\leq b<10

. Why write this way: you see the order of magnitude at a glance — the power of ten tells how many places the decimal point moved from the usual "one-digit" part.

3{,}2\cdot10^{5}=320\,000

— the decimal point "travels" together with the power of

10

The number

0{,}0045

becomes

4{,}5\cdot10^{-3}

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