Question

state whether 35/50 will have a terminating decimal expansion or a non-terminating repeating decimal

Answer 1

here is ur perfect answer in image.


hope it helps u a lot

Answer 2

Answer:

$Given \: rational\: number \\\frac{35}{50}\:is \: a \\ terminating\: decimal$

Step-by-step explanation:

$Given\: Rational\:number =\frac{35}{50}$

$Simplest \:form \: the \: number\\=\frac{5\times 7}{5\times 10}\\=\frac{7}{10}$

$Denominator \:q = 10 = 2^{1}\times 5^{1}\\is \: of\:the \:form \:2^{n}\times 5^{m}\\where \: n, m \:are \: integers$

Therefore,

$Given \: rational\: number \\\frac{35}{50}=\frac{7}{10}\\is \: a \: terminating\: decimal$

________________________

Condition:

Let x = p/q be a rational number,such that the prime factorisation of q is of the form

$2^{n}5^{m}$ ,where n and m are non-negative Integers .

Then x has a decimal expansion which terminates.

__________________________

Verification:

$\frac{35}{50}\\=\frac{7}{10}\\=0.7\:(terminating\: decimal)$

•••♪