Question

What is the decimal expansion of 3/35

Answer 1

$Given \: Rational \: number \:is \:\frac{3}{35}$

$Here \: denominator \: 35\\ = 3 \times 7 \:is \:not \:of \:the \:form \: 2^{n} \times 3^{m}$

$So, \frac{3}{35} \:is \: a\: non - terminating \:recurring \:decimal$

35)3.0000(0.0857142 857142

**** 0

________

*****30

*****00

__________

*****300

*****280

___________

*******200

******* 175

____________

********* 250

********* 245

_____________

************* 50

************* 35

______________

************** 150

************** 140

________________

*************** 100

**************** 70

_______________

***************** 30

From here process repeats.

Therefore.,

$\red {decal \:form \:of \:\frac{3}{35}} \\= 0.0857142 857142 \cdot\cdot\cdot \\=0.0\overline {857142}$

$\blue {( Non - terminating }\\\blue {and \: recurring\:decimal )}$

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