Question

Find the smallest number by which 891/3500
must be multiplied to make it a terminating decimal.​

Answer 1

Answer:- No such no. exists.

Explanation:- For the no. to have a terminating decimal ,

the denominator has to be in the form of

${2}^{n} \: \times \: \: {5}^{n } \: or \: {10}^{n}$

But in the question:-

$\frac{891}{3500} = \frac{ {9}^{2} \times 11} { {7}^{1} \times {5}^{1 } \times {10}^{3} }$

Hence, there is no such no. and this fraction does not have a terminating decimal.

Hope it helps, and please mark it as the brainliest...

Answer 2

The smallest number that should be multiplied with 891/3500 to make it a terminating decimal is 7.

Given: A fraction 891/3500 is given

To find: Smallest number that must be multiplied to make it a terminating decimal

Solution: For a fraction p/q where q is not equal to 0 to be a terminating decimal, the denominator (q) should be prime factorised in the form:

${2}^{m} \times {5}^{n}$

where m and n are whole numbers.

Here, the fraction given is 891/3500.

Prime factorisation of 3500

= 5×5×5×7×2×2

$= {5}^{3} \times {2}^{2} \times 7$

Here, 7 is an extra multiple in the prime factorisation. If the fraction is multiplied by 7, the 7 in the denominator cancels out and the prime factorisation of q comes in the form of

${2}^{m} \times {5}^{n}$