(i) Show that for any quantity written in the form , where and is an integer, the…

PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

(i) Show that for any quantity written in the form

a\times10^{n}

, where

1\le a<10

and

n

is an integer, the order of magnitude equals

n

when

1\le a<5

and equals

n+1

when

5\le a<10

. (ii) Hence find the smallest value of

a

for which the order of magnitude of

a\times10^{3}

changes from

10^{3}

10^{4}

, and illustrate your answer with numerical examples. (iii) Discuss briefly how this threshold influences quick estimations in physics problems involving approximate powers of ten.

Related theory

Measurement Systems
Significant figures and magnitude
Dimensions of physical quantities

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