Question

Which fraction has a terminating decimal as its decimal expansion? A 1/3 B 1/5 C 1/7 D 1/9

Answer 1

Option B $\bold{\frac{1}{5}}$  is the correct answer.

Given:

4 fractions in the options.

To find:

Which fraction has a terminating decimal as its decimal expansion.

Solution:

Terminating decimal means non repeating decimal, decimal number that stops after certain digits , now in the case there are 4 options given, let us first take:

$\frac{1}{3}=0.333333333333333 \ldots \ldots \ldots . .3$

In this case 3 is repeating never ending therefore not a terminating decimal

Next,  

$\frac{1}{5}=0.2$

Now as we can see that the value of$\frac{1}{5}$ does have a terminating decimal value therefore, $\frac{1}{5}$ has a terminating value.

For,  

$\frac{1}{7}$ the value is 0.142857142857………142857 the case is similar to repeating decimal, hence not the terminating decimal

$\frac{1}{9}$ the value is 0.1111111111…..11111111111 thereby again not a terminating decimal.

Therefore, the correct answer is option B. $\bold{\frac{1}{5}}$ is the fraction.

Answer 2

Answer:

$\frac{1}{5} \: is \: a \\\: terminating \: decimal$

option (B) is correct.

Step-by-step explanation:

$Let \:x=\frac{p}{q}\: be\:a\: \\Rational\:number,\:such \:that \:the\\ \:prime \: Factorisation\:of \:q\:is\:of\\\: the\:form\:2^{n}\times5^{m},\\\: where\:n,\:m\:are\: non-negative\:integers.\\ \:Then \:x\:has \:a \:decimal\\ \: expansion \:which \: terminates.$

$Here,\\In \: \frac{1}{5}\: denominator\\ \: q = 5 \: is \: of \: the \: form \: 2^{n}\times 5^{m} .$

Therefore,

$\frac{1}{5} \: is \: a \\\: terminating \: decimal$

Verification:

$\frac{1}{5} = \frac{1\times 2}{5\times 2}\\ = \frac{2}{10}\\=0.2 \: (terminating\: decimal)$

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