Question

without long division state whether 935 upon 10500 will have the terminating or non terminating repeating decimal expansion​

Answer 1

Given:

935 upon 10500

To find:

Without long division state whether it will have terminating or non terminating repeating decimal expansion.

Solution:

1) Without the long division, we can figure it out by the prime factorization of the denominator.

2) If the denominator has only factors in the form of 2ᵃ5ᵇ then only the fraction has terminating decimal expansion otherwise it will have non terminating repeating decimal expansion.

3) Prime factorization of 10500 and 935:

• 10500 = 2×2×5×5×5×3×7
• 935 = 5×187

We simplify the fraction by eliminating the common factors.

As there is no common factor for 935 and 10500 other than 5 so that won't make any difference in the answer and

the simplified fraction is 187/2100,

then,

the denominator has other than 2 and 5 that is 3 and 7 so the fraction will be non terminating and repeating decimal.

935 upon 10500 is non terminating repeating decimal expansion​

Answer 2

Step-by-step explanation:

Let x=

q

p

be a rational number, such that the prime factorisation of q is of the form 2

n

5

m

, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.

(i)

3125

13

Factorise the denominator, we get

3125=5×5×5×5×5=5

5

So, denominator is in form of 5

m

so,

3125

13

is terminating.

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