Question

without long division method ,state wether 935/10500 will have the terminating or non terminating or repeating decimal expantion​

Answer 1

Answer:

Non - terminating

Step-by-step explanation:

935/10500

-> 935 /10500= 187 / 2250

-> 187 / (5)3 *(3)2* 2

so , it can't be divide properly

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Answer 2

Step-by-step explanation:

Given that:935/10500

To check:

without long division method, find the number have the terminating or non terminating or repeating decimal expansion

Solution: Check for any common factor in numerator and denominator(Number should be simple rational number)

After inspection it is clear that,5 is common in both,cancel that

$\frac{935}{10500} \\ \\ = \frac{187}{2100}$

2) Do prime factors of denominator,if they are in the form of

${2}^{n} \times {5}^{m} \: m ,\: n \: belongs \: to \: positive \: integer$

then given number have terminating decimal expansion otherwise non-terminating repeating decimal expansion

So,

$\frac{187}{2100} \\ \\ = \frac{187}{ {2}^{2} \times 3 \times {5}^{2} \times 7 }$

Here we can easily see that

${2}^{2} \times 3 \times {5}^{2} \times 7 \: \not = {2}^{n} \times {5}^{m}$

So,given rational number(935/10500) is non-terminating repeating decimal expansion.

Hope it helps you.