Question

Which of the following has a terminating decimal expansion?
12/17
31/30
81/400

Answer 1

Terminating decimal :

Terminating decimal means , the decimal expansion of a number which ends at a particular point of the quotient .

If the value doesn't end it's called non terminating . If the value has same numbers repeating while not ending it is called as repeating non terminating decimal . If it it doesn't end and does not have repeating terms it is known as non terminating non repeating .

We have been asked to find which of the following decimals has terminating expansion meaning that which of the following will have a a specific quotient .

$\sf \: \dfrac{12}{17} \implies \cancel{\dfrac{12}{17} } = 0.70588235294........$

So as we can see 12/17 doesn't and so it is a non terminating decimal.

$\sf \: \dfrac{13}{30} \implies \cancel{ \dfrac{13}{30}} = 0.43333333333333333333......$

Here as well the terms are not ending . So this is also a non terminating decimal .

$\sf \: \dfrac{81}{400} \implies \cancel{ \dfrac{81}{400}} = 0.2025$

Here the digits are ending so it's a terminating decimal .

Answer 2

Answer:

31/30.................