Question

Without actually dividing find which of the following are terminating decimals.
i. 3/25 ii. 11/18 iii. 13/20 iv. 41/42

Answer 1

1 0.12 terminating
2. non terminating 
3. non terminating

Answer 2

Answer:

$\frac{3}{25} \: is \: terminating \\ \\ \frac{13}{20} \: is \: terminating$

Step-by-step explanation:

Without actually dividing find which of the following are terminating decimals.

i. 3/25 ii. 11/18 iii. 13/20 iv. 41/42

We know that if the denominator of rational number have the factors only 2 and 5 then only the given rational number is terminating decimal.

or the denominator can be expressed in the form of

${2}^{n} {5}^{m} \: \: \: n, m \:\epsilon \ \: N$

$1) \: \frac{3}{25} \\ \\ = \frac{3}{ {(5)}^{2} } \\ \\ hence \: number \: is \: terminating \: decimal$

$2) \frac{11}{18} \\ \\ = \frac{11}{2 \times 3 \times 3} \\ \\ = \frac{11}{2 \times {(3)}^{2} } \\ \\ = not \: terminating$

$3) \frac{13}{20} \\ \\ = \frac{13}{2 \times 2 \times 5} \\ \\ = \frac{13}{ {(2)}^{2}5 } \\ \\ = terminating \: decimal$

$4) \frac{41}{42} \\ \\ = \frac{41}{2 \times 3 \times 7} \\ \\ = non \: terminating$

Hope it helps you.